23
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. Chapter 12 A2 Glencoe Algebra 1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME DATE PERIOD Chapter 12 6 Glencoe Algebra 1 Study Guide and Intervention (continued) Designing a Survey Sampling Techniques Suppose you want to survey students about their choice of radio stations. All students make up the population you want to survey. A sample is some portion of the larger group that you select to represent the entire group. A census would include all students within the population. A random sample of a population is selected so that it is representative of the entire population. Simple Random Sample a sample that is as likely to be chosen as another from a population Stratified Random Sample A population is first divided into similar, nonoverlapping groups. A simple random sample is then chosen from each group. Systematic Random Sample Items are selected according to a specified time or interval. SCHOOL Ten students are chosen randomly from each high school class to be on an advisory committee with the principal. a. Identify the sample and suggest a population from which it was chosen. The sample is 4 groups of 10 students each from the freshmen, sophomore, junior, and senior classes. The population is the entire student body of the school. b. Classify the sample as simple, stratified, or systematic. This is a stratified random sample because the population was first divided into nonoverlapping groups and then a random sample was chosen from each group. DOOR PRIZES Each of the participants in a conference was given a numbered name tag. Twenty-five numbers were chosen at random to receive a door prize. a. Identify the sample and suggest a population from which it was chosen. The sample was 25 participants of the conference. The population was all of the participants of the conference. b. Classify the sample as simple, stratified, or systematic. Since the numbers were chosen randomly, this is a simple random sample because each participant was equally likely to be chosen. Exercises Identify each sample, suggest a population from which it was selected. Then classify the sample as simple, stratified, or systematic. Explain your reasoning. 1. SCHOOL Each student in a class of 2. GARDENING A gardener divided a lot 25 students was given a number at the into 25-square-foot sections. He then took beginning of the year. Periodically, the 2 soil samples from each and tested the teacher chooses 4 numbers at random to samples for mineral content. 2 soil display their homework on a projector. samples from each section; entire 4 students; 25 students lot; stratified in the class; simple 3. SCHOOL One hundred students in the 4. SHOPPING Every tenth person leaving a lunch room are chosen for a survey. All grocery store was asked if they would students in the school eat lunch at the participate in a community survey. every same time. 100 students; all tenth person leaving a grocery students; simple store; all shoppers at the grocery store; systematic 12-1 Example 1 Example 2 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc. NAME DATE PERIOD Lesson 12-1 Chapter 12 7 Glencoe Algebra 1 12-1 Skills Practice Designing a Survey Identify each sample, and suggest a population from which it was selected. Then classify the type of data collection used. 1. LANDSCAPING A homeowner is concerned about the quality of the topsoil in her back yard. The back yard is divided into 5 equal sections, and then a 1-inch plug of topsoil is randomly removed from each of the 5 sections. The soil is taken to a nursery and analyzed for mineral content. 5 one-inch plugs of topsoil; all the topsoil in the back yard; stratified 2. HEALTH A hospital’s administration is interested in opening a gym on the premises for all its employees. They ask each member of the night-shift emergency room staff if he or she would use the gym, and if so, what hours the employee would prefer to use it. the night-shift emergency room staff at a hospital; all employees at the hospital; convenience 3. POLITICS A senator wants to know her approval rating among the constituents in her state. She sends questionnaires to the households of 1000 registered voters. a group of registered voters in a state; all registered voters in the state; voluntary response Identify each sample as biased or unbiased. Explain your reasoning. 4. MANUFACTURING A company that produces motherboards for computers randomly selects 25 boxed motherboards out of a shipment of 1500, and then tests each selected motherboard to see that it meets specifications. Unbiased; the sample is representative and randomly chosen. 5. GOVERNMENT The first 100 people entering a county park on Thursday are asked their opinions on a proposed county ordinance that would allow dogs in county parks to go unleashed in certain designated areas. Biased; the convienience sample may not accurately reflect the population. Identify the sample and suggest a population from which it was selected. Then classify the sample as simple, stratified, or systematic. Explain your reasoning. 6. MUSIC To determine the music preferences of their customers, the owners of a music store randomly choose 10 customers to participate in an in-store interview in which they listen to new CDs from artists in all music categories. 10 music-store customers; all customers in a music store; simple; sample is equally likely to be chosen as any other sample from the population 7. LIBRARIES A community library asks every tenth patron who enters the library to name the type or genre of book he or she is most likely to borrow. They conduct the interviews from opening to closing on three days of the week. They will use the data for new acquisitions. a group of library patrons; all patrons of a library; systematic; individuals are selected according to a specified interval 8. COMPUTERS To determine the number of students who use computers at home, the high school office chooses 10 students at random from each grade, and then interviews the students. 10 students from each grade of a high school; all students in the high school; stratified; the population is first divided into similar, nonover lapping groups Answers (Lesson 12-1)

Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

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Page 1: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A2 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

6

Gle

ncoe A

lgeb

ra 1

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n (continued)

Desig

nin

g a

Su

rvey

Sam

plin

g T

ech

niq

ues

Su

pp

ose

you

wan

t to

su

rvey s

tud

en

ts a

bou

t th

eir

ch

oic

e o

f ra

dio

sta

tion

s. A

ll s

tud

en

ts m

ak

e u

p t

he p

op

ula

tio

n y

ou

wan

t to

su

rvey.

A s

am

ple

is

som

e

port

ion

of

the l

arg

er

gro

up

th

at

you

sele

ct t

o r

ep

rese

nt

the e

nti

re g

rou

p.

A c

en

su

s w

ou

ld

incl

ud

e a

ll s

tud

en

ts w

ith

in t

he p

op

ula

tion

. A

ra

nd

om

sa

mp

le o

f a p

op

ula

tion

is

sele

cted

so

that

it i

s re

pre

sen

tati

ve o

f th

e e

nti

re p

op

ula

tion

.

Sim

ple

Ran

do

m S

am

ple

a s

am

ple

that

is a

s lik

ely

to b

e c

hosen a

s a

noth

er

from

a p

opula

tion

Str

ati

fied

Ran

do

m S

am

ple

A p

opula

tion is f

irst

div

ided into

sim

ilar,

nonoverlappin

g g

roups.

A s

imple

random

sam

ple

is t

hen c

hosen f

rom

each g

roup.

Syste

mati

c R

an

do

m S

am

ple

Item

s a

re s

ele

cte

d a

ccord

ing t

o a

specifie

d t

ime o

r in

terv

al.

S

CH

OO

L T

en

stu

den

ts

are c

ho

sen

ra

nd

om

ly f

ro

m e

ach

hig

h

sch

oo

l cla

ss t

o b

e o

n a

n a

dv

iso

ry

co

mm

itte

e w

ith

th

e p

rin

cip

al.

a.

Iden

tify

th

e s

am

ple

an

d s

ug

gest

a

po

pu

lati

on

fro

m w

hic

h i

t w

as

ch

osen

.

Th

e s

am

ple

is

4 g

rou

ps

of

10 s

tud

en

ts

each

fro

m t

he f

resh

men

, so

ph

om

ore

,

jun

ior,

an

d s

en

ior

class

es.

Th

e p

op

ula

tion

is t

he e

nti

re s

tud

en

t bod

y o

f th

e s

chool.

b.

Cla

ssif

y t

he s

am

ple

as sim

ple

,

stratified,

or systematic.

Th

is i

s a s

trati

fied r

an

dom

sam

ple

beca

use

the p

opu

lati

on

was

firs

t div

ided i

nto

non

overl

appin

g g

rou

ps

an

d t

hen

a r

an

dom

sam

ple

was

chose

n f

rom

each

gro

up.

D

OO

R P

RIZ

ES

E

ach

of

the p

arti

cip

an

ts i

n a

co

nfe

ren

ce w

as

giv

en

a n

um

bered

na

me t

ag

.

Tw

en

ty-f

ive n

um

bers w

ere c

ho

sen

at

ra

nd

om

to

receiv

e a

do

or p

riz

e.

a.

Iden

tify

th

e s

am

ple

an

d s

ug

gest

a

po

pu

lati

on

fro

m w

hic

h i

t w

as

ch

osen

.

Th

e s

am

ple

was

25 p

art

icip

an

ts o

f th

e

con

fere

nce

. T

he p

op

ula

tion

was

all

of

the

part

icip

an

ts o

f th

e c

on

fere

nce

.

b.

Cla

ssif

y t

he s

am

ple

as sim

ple

,

stratified

, o

r systematic.

Sin

ce t

he n

um

bers

were

ch

ose

n

ran

dom

ly,

this

is

a s

imp

le r

an

dom

sam

ple

beca

use

each

part

icip

an

t w

as

equ

all

y l

ikely

to b

e c

hose

n.

Exerc

ises

Iden

tify

ea

ch

sa

mp

le,

su

gg

est

a p

op

ula

tio

n f

ro

m w

hic

h i

t w

as s

ele

cte

d.

Th

en

cla

ssif

y t

he s

am

ple

as sim

ple

, stratified

, o

r systematic.

Ex

pla

in y

ou

r r

ea

so

nin

g.

1. S

CH

OO

L E

ach

stu

den

t in

a c

lass

of

2.

GA

RD

EN

ING

A

gard

en

er

div

ided

a l

ot

25 s

tud

en

ts w

as

giv

en

a n

um

ber

at

the

in

to 2

5-s

qu

are

-foot

sect

ion

s. H

e t

hen

took

begin

nin

g o

f th

e y

ear.

Peri

od

icall

y,

the

2 s

oil

sam

ple

s fr

om

each

an

d t

est

ed

th

e

teach

er

choose

s 4 n

um

bers

at

ran

dom

to

sa

mp

les

for

min

era

l co

nte

nt.

2 s

oil

dis

pla

y t

heir

hom

ew

ork

on

a p

roje

ctor.

sam

ple

s f

rom

each

secti

on

; en

tire

4 s

tud

en

ts;

25 s

tud

en

ts

lot;

str

ati

fied

in t

he c

lass;

sim

ple

3. S

CH

OO

L O

ne h

un

dre

d s

tud

en

ts i

n t

he

4.

SH

OP

PIN

G E

very

ten

th p

ers

on

leavin

g a

lun

ch r

oom

are

ch

ose

n f

or

a s

urv

ey.

All

gro

cery

sto

re w

as

ask

ed

if

they w

ou

ld

stu

den

ts i

n t

he s

chool

eat

lun

ch a

t th

e

p

art

icip

ate

in

a c

om

mu

nit

y s

urv

ey.

every

sam

e t

ime.

100 s

tud

en

ts;

all

te

nth

pers

on

leavin

g a

gro

cery

stu

den

ts;

sim

ple

sto

re;

all s

ho

pp

ers

at

the g

rocery

sto

re;

syste

mati

c

12-1

Exam

ple

1Exam

ple

2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-1

Ch

ap

ter

12

7

Gle

ncoe A

lgeb

ra 1

12-1

Sk

ills

Pra

ctic

e

Desig

nin

g a

Su

rvey

Iden

tify

ea

ch

sa

mp

le,

an

d s

ug

gest

a p

op

ula

tio

n f

ro

m w

hic

h i

t w

as s

ele

cte

d.

Th

en

cla

ssif

y t

he t

yp

e o

f d

ata

co

llecti

on

used

.

1. LA

ND

SC

AP

ING

A

hom

eow

ner

is c

on

cern

ed

abou

t th

e q

uali

ty o

f th

e t

op

soil

in

her

back

yard

. T

he b

ack

yard

is

div

ided

in

to 5

equ

al

sect

ion

s, a

nd

th

en

a 1

-in

ch p

lug o

f to

pso

il i

s

ran

dom

ly r

em

oved

fro

m e

ach

of

the 5

sect

ion

s. T

he s

oil

is

tak

en

to a

nu

rsery

an

d

an

aly

zed

for

min

era

l co

nte

nt.

5 o

ne-i

nch

plu

gs o

f to

pso

il;

all t

he t

op

so

il i

n

the b

ack y

ard

; str

ati

fied

2. H

EA

LT

H A

hosp

ital’s

ad

min

istr

ati

on

is

inte

rest

ed

in

op

en

ing a

gym

on

th

e p

rem

ises

for

all

its

em

plo

yees.

Th

ey a

sk e

ach

mem

ber

of

the n

igh

t-sh

ift

em

erg

en

cy r

oom

sta

ff i

f h

e o

r

she w

ou

ld u

se t

he g

ym

, an

d i

f so

, w

hat

hou

rs t

he e

mp

loyee w

ou

ld p

refe

r to

use

it.

th

e n

igh

t-sh

ift

em

erg

en

cy r

oo

m s

taff

at

a h

osp

ital;

all e

mp

loyees a

t th

e

ho

sp

ital;

co

nven

ien

ce

3. P

OLIT

ICS

A

sen

ato

r w

an

ts t

o k

now

her

ap

pro

val

rati

ng a

mon

g t

he c

on

stit

uen

ts i

n h

er

state

. S

he s

en

ds

qu

est

ion

nair

es

to t

he h

ou

seh

old

s of

1000 r

egis

tere

d v

ote

rs.

a g

rou

p o

f re

gis

tere

d v

ote

rs i

n a

sta

te;

all r

eg

iste

red

vo

ters

in

th

e s

tate

; vo

lun

tary

resp

on

se

Iden

tify

ea

ch

sa

mp

le a

s biased

or unbiased

. E

xp

lain

yo

ur r

ea

so

nin

g.

4. M

AN

UFA

CT

UR

ING

A

com

pan

y t

hat

pro

du

ces

moth

erb

oard

s fo

r co

mp

ute

rs r

an

dom

ly

sele

cts

25 b

oxed

moth

erb

oard

s ou

t of

a s

hip

men

t of

1500,

an

d t

hen

test

s each

sele

cted

moth

erb

oard

to s

ee t

hat

it m

eets

sp

eci

fica

tion

s. U

nb

iased

; th

e s

am

ple

is

rep

resen

tati

ve a

nd

ran

do

mly

ch

osen

.

5. G

OV

ER

NM

EN

T T

he f

irst

100 p

eop

le e

nte

rin

g a

cou

nty

park

on

Th

urs

day a

re a

sked

their

op

inio

ns

on

a p

rop

ose

d c

ou

nty

ord

inan

ce t

hat

wou

ld a

llow

dogs

in c

ou

nty

park

s to

go u

nle

ash

ed

in

cert

ain

desi

gn

ate

d a

reas.

B

iased

; th

e c

on

vie

nie

nce s

am

ple

may

no

t accu

rate

ly r

efl

ect

the p

op

ula

tio

n.

Iden

tify

th

e s

am

ple

an

d s

ug

gest

a p

op

ula

tio

n f

ro

m w

hic

h i

t w

as s

ele

cte

d.

Th

en

cla

ssif

y t

he s

am

ple

as sim

ple

, stratified

, o

r systematic. E

xp

lain

yo

ur r

ea

so

nin

g.

6. M

US

IC T

o d

ete

rmin

e t

he m

usi

c p

refe

ren

ces

of

their

cu

stom

ers

, th

e o

wn

ers

of

a m

usi

c

store

ran

dom

ly c

hoose

10 c

ust

om

ers

to p

art

icip

ate

in

an

in

-sto

re i

nte

rvie

w i

n w

hic

h t

hey

list

en

to n

ew

CD

s fr

om

art

ists

in

all

mu

sic

cate

gori

es.

10 m

usic

-sto

re c

usto

mers

; all c

usto

mers

in

a m

usic

sto

re;

sim

ple

; sam

ple

is e

qu

ally l

ikely

to

be c

ho

sen

as a

ny o

ther

sam

ple

fro

m t

he

po

pu

lati

on

7. LIB

RA

RIE

S A

com

mu

nit

y l

ibra

ry a

sks

every

ten

th p

atr

on

wh

o e

nte

rs t

he l

ibra

ry t

o

nam

e t

he t

yp

e o

r gen

re o

f book

he o

r sh

e i

s m

ost

lik

ely

to b

orr

ow

. T

hey c

on

du

ct t

he

inte

rvie

ws

from

op

en

ing t

o c

losi

ng o

n t

hre

e d

ays

of

the w

eek

. T

hey w

ill

use

th

e d

ata

for

new

acq

uis

itio

ns.

a g

rou

p o

f lib

rary

patr

on

s;

all p

atr

on

s o

f a l

ibra

ry;

syste

mati

c;

ind

ivid

uals

are

sele

cte

d a

cco

rdin

g t

o a

sp

ecif

ied

in

terv

al

8. C

OM

PU

TE

RS

T

o d

ete

rmin

e t

he n

um

ber

of

stu

den

ts w

ho u

se c

om

pu

ters

at

hom

e,

the

hig

h s

chool

off

ice c

hoose

s 10 s

tud

en

ts a

t ra

nd

om

fro

m e

ach

gra

de,

an

d t

hen

in

terv

iew

s

the s

tud

en

ts.

10 s

tud

en

ts f

rom

each

gra

de o

f a h

igh

sch

oo

l; a

ll s

tud

en

ts

in t

he h

igh

sch

oo

l; s

trati

fied

; th

e p

op

ula

tio

n i

s f

irst

div

ided

in

to s

imilar,

n

on

over

lap

pin

g g

rou

ps

Answers (Lesson 12-1)

Page 2: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A3 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

8

Gle

ncoe A

lgeb

ra 1

12-1

Practi

ce

Desig

nin

g a

Su

rvey

Iden

tify

ea

ch

sa

mp

le,

su

gg

est

a p

op

ula

tio

n f

ro

m w

hic

h i

t w

as s

ele

cte

d.

Th

en

cla

ssif

y t

he t

yp

e o

f d

ata

co

llecti

on

used

.

1. G

OV

ER

NM

EN

T A

t a t

ow

n c

ou

nci

l m

eeti

ng,

the c

hair

ask

s 5 c

itiz

en

s att

en

din

g f

or

their

op

inio

ns

on

wh

eth

er

to a

pp

rove r

ezon

ing f

or

a r

esi

den

tial

are

a.

5 c

itiz

en

s o

f a t

ow

n;

all c

itiz

en

s o

f a t

ow

n;

bia

sed

; co

nven

ien

ce

2. B

OT

AN

Y T

o d

ete

rmin

e t

he e

xte

nt

of

leaf

bli

gh

t in

th

e m

ap

le t

rees

at

a n

atu

re p

rese

rve,

a b

ota

nis

t d

ivid

es

the r

ese

rve i

nto

10 s

ect

ion

s, r

an

dom

ly s

ele

cts

a 2

00-f

oot

by 2

00-f

oot

squ

are

in

th

e s

ect

ion

, an

d t

hen

exam

ines

all

th

e m

ap

le t

rees

in t

he s

ect

ion

. th

e m

ap

le

trees i

n a

sq

uare

are

a o

f each

of

10 s

ecti

on

s a

t a n

atu

re p

reserv

e;

all t

he

map

le t

rees a

t th

e n

atu

re p

reserv

e;

un

bia

sed

; str

ati

fied

3. FIN

AN

CE

S T

o d

ete

rmin

e t

he p

op

ula

rity

of

on

lin

e b

an

kin

g i

n t

he U

nit

ed

Sta

tes,

a

poll

ing c

om

pan

y s

en

ds

a m

ail

-in

su

rvey t

o 5

000 a

du

lts

to s

ee i

f th

ey b

an

k o

nli

ne,

an

d i

f

they d

o,

how

man

y t

imes

they b

an

k o

nli

ne e

ach

mon

th.

5000 U

.S.

ad

ult

s;

all U

.S.

ad

ult

s;

bia

sed

; vo

lun

tary

resp

on

se

Iden

tify

ea

ch

sa

mp

le a

s b

iased

or u

nb

iased

. E

xp

lain

yo

ur r

ea

so

nin

g.

4. S

HO

ES

A

sh

oe m

an

ufa

ctu

rer

wan

ts t

o c

heck

th

e q

uali

ty o

f it

s sh

oes.

Every

tw

en

ty

min

ute

s, 2

0 p

air

s of

shoes

are

pu

lled

off

th

e a

ssem

bly

lin

e f

or

a q

uali

ty

insp

ect

ion

. u

nb

iased

; th

e s

am

ple

is s

yste

mati

cally c

ho

sen

5. B

US

INE

SS

T

o l

earn

wh

ich

ben

efi

ts e

mp

loyees

at

a l

arg

e c

om

pan

y t

hin

k a

re m

ost

imp

ort

an

t, t

he m

an

agem

en

t h

as

a c

om

pu

ter

sele

ct 5

0 e

mp

loyees

at

ran

dom

. T

he

em

plo

yees

are

th

en

in

terv

iew

ed

by t

he H

um

an

Rela

tion

s d

ep

art

men

t. u

nb

iased

; th

e

sam

ple

is r

an

do

m

Fo

r Q

uesti

on

6, id

en

tify

th

e s

am

ple

, a

nd

su

gg

est

a

po

pu

lati

on

fro

m w

hic

h i

t

wa

s s

ele

cte

d. T

hen

cla

ssif

y t

he s

am

ple

as s

imp

le, st

ra

tifi

ed

, o

r s

yst

em

ati

c. E

xp

lain

yo

ur r

ea

so

nin

g.

6. B

US

INE

SS

A

n i

nsu

ran

ce c

om

pan

y c

heck

s every

hu

nd

red

th c

laim

paym

en

t to

en

sure

that

claim

s h

ave b

een

pro

cess

ed

corr

ect

ly.

every

hu

nd

red

th c

laim

paym

en

t at

an

in

su

ran

ce c

om

pan

y;

all c

laim

paym

en

ts a

t an

in

su

ran

ce c

om

pan

y;

syste

mati

c;

the s

am

ple

was s

ele

cte

d a

cco

rdin

g t

o a

sp

ecif

ied

in

terv

al

7. E

NV

IRO

NM

EN

T S

up

pose

you

wan

t to

kn

ow

if

a m

an

ufa

ctu

rin

g p

lan

t is

dis

charg

ing

con

tam

inan

ts i

nto

a l

oca

l ri

ver.

Desc

ribe a

n u

nbia

sed

way i

n w

hic

h y

ou

cou

ld c

heck

th

e

river

wate

r fo

r co

nta

min

an

ts.

Sam

ple

an

sw

er:

At

a d

iffe

ren

t ti

me e

ach

day,

take a

10-o

un

ce s

am

ple

of

wate

r fr

om

giv

en

lo

cati

on

s j

ust

up

str

eam

an

d

just

do

wn

str

eam

fro

m w

here

th

e p

lan

t d

isch

arg

es i

ts w

aste

s.

Co

mp

are

th

e s

am

ple

s f

or

co

nta

min

an

ts t

o s

ee i

f an

y a

re e

nte

rin

g t

he r

iver

fro

m t

he

dis

ch

arg

e.

8. S

CH

OO

L S

up

pose

you

wan

t to

kn

ow

th

e i

ssu

es

most

im

port

an

t to

teach

ers

at

you

r

sch

ool.

Desc

ribe a

n u

nbia

sed

way i

n w

hic

h y

ou

cou

ld c

on

du

ct y

ou

r su

rvey.

Sam

ple

an

sw

er:

Ob

tain

a l

ist

of

all t

each

ers

at

the s

ch

oo

l. A

ssig

n e

ach

teach

er

a n

um

ber,

an

d t

hen

ran

do

mly

sele

ct

10 n

um

bers

. In

terv

iew

each

of

the

teach

ers

assig

ned

on

e o

f th

e s

ele

cte

d n

um

bers

.

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-1

Ch

ap

ter

12

9

Gle

ncoe A

lgeb

ra 1

12-1

Wo

rd

Pro

ble

m P

racti

ce

Desig

nin

g a

Su

rvey

F

or E

xercis

es 1

–4,

iden

tify

th

e s

am

ple

an

d t

he p

op

ula

tio

n f

ro

m w

hic

h i

t w

as

sele

cte

d,

an

d s

tate

wh

eth

er i

t is

bia

sed

or u

nb

iased

. If

un

bia

sed

, cla

ssif

y t

he

sa

mp

le a

s s

imp

le,

str

ati

fied

, o

r

syste

ma

tic.

If b

iased

, cla

ssif

y a

s

con

ven

ien

ce o

r v

olu

nta

ry r

esp

on

se.

Ex

pla

in y

ou

r r

ea

so

nin

g.

1. S

CH

OO

L M

s. Y

eon

g c

hoose

s fo

ur

stu

den

ts t

o p

ass

ou

t sn

ack

s each

day.

To c

hoose

th

e s

tud

en

ts,

she w

rite

s th

e

nam

es

of

each

of

her

18 s

tud

en

ts o

n

small

pie

ces

of

pap

er,

an

d p

lace

s th

em

in

a c

up

. S

he m

ixes

up

th

e n

am

es

an

d p

ull

s

ou

t fo

ur

to b

e t

he s

nack

help

ers

.

sam

ple

: 4 h

elp

ers

; p

op

ula

tio

n:

the

18 s

tud

en

ts i

n t

he c

lass;

un

bia

sed

, sim

ple

ran

do

m s

am

ple

2. E

LE

CT

ION

S In

Su

mm

erv

ille

, re

sid

en

ts

vote

for

mayor

at

on

e o

f th

e e

igh

t

pre

cin

ct v

oti

ng p

lace

s n

ear

wh

ere

th

ey

live.

To a

cqu

ire e

arl

y e

lect

ion

resu

lts

for

the e

ven

ing n

ew

s, a

rep

ort

er

stan

ds

ou

tsid

e o

ne o

f th

e c

ity’s

eig

ht

voti

ng

stati

on

s an

d a

sks

as

man

y p

eop

le a

s

poss

ible

for

wh

om

th

ey v

ote

d.

sam

ple

: th

e v

ote

rs t

he r

ep

ort

er

inte

rvie

ws;

po

pu

lati

on

: all v

ote

rs;

bia

sed

, co

nven

ien

ce s

am

ple

3. D

ISE

AS

E A

Eu

rop

ean

cou

ntr

y’s

healt

h

dep

art

men

t u

ses

nets

to t

rap

bir

ds

near

a l

oca

l w

ild

life

refu

ge.

Th

e b

ird

is

test

ed

for

the p

rese

nce

of

the a

via

n f

lu v

iru

s.

sam

ple

: b

ird

s c

ap

ture

d;

po

pu

lati

on

: b

ird

s i

n t

he r

eg

ion

; b

iased

, co

nven

ien

ce s

am

ple

4. S

OIL

T

o c

heck

for

the p

rese

nce

of

harm

ful

chem

icals

in

th

e g

rou

nd

at

a

new

con

stru

ctio

n s

ite,

geote

chn

ical

en

gin

eers

div

ide t

he s

ite i

nto

12

rect

an

gu

lar

are

as

an

d r

em

ove a

pin

t of

soil

fro

m e

ach

are

a f

or

test

ing.

sam

ple

: 12 p

t o

f so

il;

po

pu

lati

on

: all o

f th

e s

oil o

n t

he s

ite;

un

bia

sed

, str

ati

fied

ran

do

m s

am

ple

5. C

HIL

D S

AFE

TY

T

he B

riti

sh C

olu

mbia

Au

tom

obil

e A

ssoci

ati

on

perf

orm

ed

a f

ree

chil

d s

afe

ty s

eat

insp

ect

ion

for

peop

le

that

cam

e i

n f

or

the s

afe

ty c

heck

. O

nly

7%

of

the 1

000 s

eats

in

spect

ed

were

pro

perl

y u

sed

. T

he g

rap

h b

elo

w s

how

s

the a

pp

roxim

ate

perc

en

tages

of

resu

lts

for

the s

afe

ty s

eat

insp

ect

ion

s.

So

urc

e:

Auto

net

a.

Wri

te a

sta

tem

en

t to

desc

ribe t

he

sam

pli

ng t

ech

niq

ue. T

he s

am

ple

is

bia

sed

becau

se i

t w

as b

ased

o

n v

olu

nta

ry r

esp

on

se.

b.

Is i

t ap

pro

pri

ate

to s

ay t

hat

23%

of

chil

dre

n i

n c

hil

d s

afe

ty s

eats

in

Bri

tish

Colu

mbia

are

not

secu

rely

fast

en

ed

in

th

eir

seat?

Exp

lain

. N

o.

Th

is w

as n

ot

a r

an

do

m s

am

ple

, so

th

e d

ata

can

no

t b

e

gen

era

lized

to

th

e p

op

ula

tio

n.

We d

o n

ot

kn

ow

ho

w t

he s

eats

are

bein

g u

sed

in

veh

icle

s t

hat

were

no

t b

rou

gh

t in

.

Ch

ild

Safe

ty S

eat

Su

rvey R

esu

lts

Child

seat

not

tightly

secure

d in v

ehic

le44%

Child

not

secure

lyfa

ste

ned

in s

eat

23%

Teth

ers

not

used

corr

ectly

14%

Incorr

ect

pla

cem

ent

of

should

er

harn

ess

9%

Seat

pro

perly u

sed

7%

Child

in incorr

ect

seat

for

age/s

ize/w

eig

ht

3%

Answers (Lesson 12-1)

Page 3: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A4 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

10

Gle

ncoe A

lgeb

ra 1

12-1

En

rich

men

t

Head

s o

r Tails

Base

d o

n t

he w

ay c

ert

ain

coin

s are

man

ufa

ctu

red

, th

ere

is

a ‘bia

s’ t

ow

ard

s la

nd

ing e

ith

er

head

s u

p o

r ta

ils

up

wh

en

bala

nce

d o

n t

heir

ed

ges.

Bala

nce

severa

l p

en

nie

s fr

om

th

e s

am

e

min

tin

g y

ear

on

th

eir

ed

ges

on

a t

able

. G

en

tly s

hak

e t

he t

able

so t

hat

the p

en

nie

s fa

ll f

lat.

1. W

hat

perc

en

t of

the p

en

nie

s w

ou

ld y

ou

exp

ect

to l

an

d h

ead

s u

p?

Sam

ple

an

sw

er:

50%

2. W

hat

perc

en

t act

uall

y l

an

ded

head

s u

p?

S

ee s

tud

en

ts’

wo

rk,

bu

t it

sh

ou

ld b

e

mo

re h

ead

s t

han

tails.

Rep

eat

the e

xp

eri

men

t.

3. W

ere

th

e r

esu

lts

sim

ilar

to y

ou

r p

revio

us

att

em

pt?

S

ee s

tud

en

ts’

wo

rk.

Th

ey

sh

ou

ld b

e s

imilar.

4. M

ak

e a

con

ject

ure

as

to w

hy t

he p

erc

en

t of

pen

nie

s th

at

lan

d f

ace

up

dif

fers

fro

m w

hat

you

wou

ld e

xp

ect

it

to b

e.

S

am

ple

an

sw

er:

mo

re w

eig

ht

on

on

e s

ide,

gro

oves

in t

he p

en

ny.

Wh

en

a p

en

ny i

s m

an

ufa

ctu

red

, it

is

bevele

d o

r gro

oved

sli

gh

tly,

so t

hat

wh

en

it

fall

s,

it i

s m

ore

lik

ely

to f

all

head

s u

p.

Th

ere

ap

pears

to b

e a

dif

fere

nce

betw

een

min

tin

g y

ears

.

Rep

eat

this

exp

eri

men

t w

ith

oth

er

min

tin

g y

ears

.

5. A

re t

he r

esu

lts

abou

t th

e s

am

e a

s befo

re?

Exp

lain

wh

y o

r w

hy n

ot.

See s

tud

en

ts’

wo

rk.

Beca

use

of

this

bia

s, t

oss

ing a

coin

an

d l

ett

ing i

t h

it t

he g

rou

nd

or

a t

able

to d

ete

rmin

e

a w

inn

er

is n

ot

fair

. T

he p

en

ny i

s m

ost

lik

ely

to l

an

d w

ith

th

e h

ead

sid

e u

p.

6. H

ow

can

you

ch

an

ge a

coin

toss

, so

th

at

head

s an

d t

ail

s are

more

equ

all

y l

ikely

to a

pp

ear?

S

am

ple

an

sw

er:

C

atc

h i

t b

efo

re i

t h

its t

he g

rou

nd

; fi

nd

a

bala

nced

co

in

Try

th

is e

xp

eri

men

t w

ith

oth

er

coin

s to

dete

rmin

e i

f th

ere

is

a “

bia

s” i

n m

an

ufa

ctu

rin

g

these

coin

s as

well

.

7. E

xp

lain

wh

at

hap

pen

s w

hen

you

try

th

is e

xp

eri

men

t w

ith

a n

ick

el,

a d

ime,

an

d

a q

uart

er.

S

ee s

tud

en

ts’

wo

rk.

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-2

Ch

ap

ter

12

11

Gle

ncoe A

lgeb

ra 1

12-2

Su

mm

ari

ze S

urv

ey R

esu

lts

To m

ak

e s

urv

ey d

ata

more

use

ful,

it

can

be s

um

mari

zed

acc

ord

ing t

o m

easu

res

of

cen

tral

ten

den

cy:

mea

n,

med

ian

, an

d m

od

e.

Typ

eD

escri

pti

on

Mo

st

Usefu

l W

hen

mean

the s

um

of

the d

ata

div

ided b

y t

he n

um

ber

of

item

s

in t

he d

ata

set

The d

ata

sets

have n

o o

utlie

rs.

media

nth

e m

iddle

num

ber

of

the o

rdere

d d

ata

, or

the m

ean

of

the m

iddle

tw

o n

um

bers

The d

ata

sets

have n

o o

utlie

rs,

but

there

are

no b

ig g

aps in t

he m

iddle

of

the d

ata

.

mode

the n

um

ber

or

num

bers

that

occur

the m

ost

oft

en

The d

ata

set

has m

any r

epeate

d n

um

bers

.

W

hic

h m

ea

su

re o

f cen

tra

l te

nd

en

cy

best

rep

resen

ts t

he d

ata

?

Ju

sti

fy y

ou

r a

nsw

er.

Th

en

fin

d t

he m

ea

su

re.

a.

RESTA

UR

AN

TS

A

resta

ura

nt

reco

rd

s t

he n

um

ber o

f p

eo

ple

wh

o o

rd

er s

ou

p a

t

lun

ch

ea

ch

da

y:

{26,

25,

30,

32,

27,

28}.

Lis

t th

e v

alu

es

from

least

to g

reate

st:

25,

26,

27,

28,

30,

32.

Th

e d

ata

set

does

not

have

an

y o

utl

iers

, an

d d

oes

not

have a

ny r

ep

eate

d n

um

bers

. T

he m

ean

wou

ld b

est

rep

rese

nt

the d

ata

.

25 +

26 +

27

+ 2

8 +

30

+ 3

2

−−

6

=

28

Th

e m

ean

of

the d

ata

is

28.

b.

SO

CC

ER

A

so

ccer t

ea

m k

eep

s a

reco

rd

of

the n

um

ber o

f p

oin

ts i

t sco

res i

n e

ach

ga

me:

{2,

3,

2,

1,

4,

3,

1,

3,

3,

4}.

Lis

t th

e v

alu

es

from

least

to g

reate

st:

1,

1,

2,

2,

3,

3,

3,

3,

4,

4.

Th

e d

ata

set

has

fou

r se

ts

of

rep

eate

d n

um

bers

. T

he m

od

e b

est

rep

rese

nts

th

e d

ata

.

Th

e m

od

e i

s 3,

the n

um

ber

that

occ

urs

th

e m

ost

oft

en

.

Exerc

ises

Wh

ich

mea

su

re o

f cen

tra

l te

nd

en

cy

best

rep

resen

ts t

he d

ata

? J

usti

fy y

ou

r a

nsw

er.

Th

en

fin

d t

he m

ea

su

re.

1. D

EFEC

TS

A

fu

rnit

ure

man

ufa

ctu

rer

keep

s re

cord

s of

how

man

y u

nit

s are

defe

ctiv

e e

ach

day:

{7,

12,

9,

8,

10,

14,

8}.

2. SC

IEN

CE T

ESTS

M

r. W

hart

on

reco

rds

his

stu

den

ts’ sc

ore

s on

th

e l

ast

sci

en

ce t

est

:

{94,

88,

88,

94,

94,

84,

94,

88,

84,

94}.

3. PU

PPIE

S A

vete

rin

ari

an

keep

s re

cord

s of

the w

eig

hts

of

pu

pp

ies

in o

un

ces:

{4.1

, 3.8

, 5.0

, 4.6

, 5.6

, 4.7

, 11.6

}.

4. C

OM

MU

TIN

G T

he l

oca

l n

ew

spap

er

con

du

cted

a t

ele

ph

on

e s

urv

ey o

f co

mm

ute

rs t

o s

ee

how

th

ey g

et

to w

ork

each

day.

Th

e r

esp

on

ses

were

: co

mm

ute

r ra

il,

22;

bu

s, 1

7;

subw

ay,

18;

walk

ing,

15;

car,

224.

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n

An

aly

zin

g S

urv

ey R

esu

lts

Exam

ple

mean

, ap

pro

xim

ate

ly 9

.7

mo

de,

94

med

ian

, 4.7

med

ian

, 18

Answers (Lesson 12-1 and Lesson 12-2)

Page 4: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A5 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

12

Gle

ncoe A

lgeb

ra 1

12-2

Evalu

ate

Su

rvey R

esu

lts

Aft

er

a s

urv

ey’s

data

has

been

su

mm

ari

zed

an

d a

rep

ort

of

the f

ind

ings

an

d c

on

clu

sion

s h

as

been

mad

e,

it i

s im

port

an

t to

be a

ble

to j

ud

ge t

he

reli

abil

ity o

f th

e r

ep

ort

. Y

ou

can

do t

his

by v

eri

fyin

g t

hat

the s

am

ple

is

tru

ly r

an

dom

, th

at

the s

am

ple

is

larg

e e

nou

gh

to b

e a

n a

ccu

rate

rep

rese

nta

tive o

f th

e p

op

ula

tion

, an

d t

hat

the

sou

rce o

f th

e d

ata

is

a r

eli

able

on

e.

Als

o c

heck

gra

ph

s acc

om

pan

yin

g s

urv

eys

for

mis

lead

ing

resu

lts.

MU

SIC

G

iven

th

e f

oll

ow

ing

po

rti

on

of

a s

urv

ey

rep

ort,

ev

alu

ate

th

e

va

lid

ity

of

the i

nfo

rm

ati

on

an

d c

on

clu

sio

n.

Qu

esti

on

: W

ha

t is

yo

ur f

av

orit

e b

an

d?

Sa

mp

le:

100 c

on

certg

oers w

ere r

an

do

mly

sele

cte

d.

Co

nclu

sio

n:

Am

eric

a’s

fa

vo

rit

e b

an

d i

s O

cto

ber H

op

e.

So

urc

e:

Octo

ber

Hope F

an C

lub

Th

e r

ep

ort

says

that

con

cert

goers

were

ch

ose

n r

an

dom

ly,

bu

t th

ere

is

no g

uara

nte

e t

hat

a

gro

up

of

con

cert

goers

is

rep

rese

nta

tive o

f A

meri

ca a

s a w

hole

. In

ad

dit

ion

, a s

am

ple

siz

e o

f

100 m

ay b

e t

oo s

mall

to d

raw

a c

on

clu

sion

fro

m.

Als

o,

the r

ep

ort

’s s

ou

rce i

s th

e “

Oct

ober

Hop

e F

an

Clu

b,”

wh

ich

may b

e b

iase

d,

con

sid

eri

ng

that

the r

ep

ort

cit

es

Oct

ober

Hop

e a

s A

meri

ca’s

favori

te b

an

d.

Exerc

ises

Giv

en

th

e f

oll

ow

ing

po

rti

on

of

a s

urv

ey

rep

ort,

ev

alu

ate

th

e v

ali

dit

y o

f th

e

info

rm

ati

on

an

d c

on

clu

sio

n.

1. SC

HO

OL U

NIF

OR

MS

S

urv

ey U

SA

poll

ed

500 r

an

dom

ly s

ele

cted

ad

ult

s in

Cin

cin

nati

,

Oh

io,

by t

ele

ph

on

e.

Q

uest

ion

: S

hou

ld p

ubli

c sc

hool

stu

den

ts w

ear

un

iform

s?

R

esu

lts:

sh

ou

ld,

58%

; sh

ou

ld n

ot,

36%

; n

ot

sure

, 6%

C

on

clu

sion

: A

du

lts

in C

inci

nn

ati

beli

eve s

tud

en

ts s

hou

ld w

ear

un

iform

s to

sch

ool.

2. ELEC

TIO

NS

S

tate

Rep

rese

nta

tive B

eck

com

mis

sion

ed

a p

oll

of

400 r

an

dom

ly s

ele

cted

ad

ult

s vis

itin

g a

mall

in

her

dis

tric

t.

Q

uest

ion

: D

o y

ou

ap

pro

ve o

f th

e j

ob S

tate

Rep

rese

nta

tive B

eck

is

doin

g?

R

esu

lts:

yes,

44%

; n

o,

32%

; u

nd

eci

ded

, 24%

C

on

clu

sion

: S

en

ato

r B

eck

wil

l w

in r

e-e

lect

ion

.

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n (continued)

An

aly

zin

g S

urv

ey R

esu

lts

Exam

ple

Resu

lts

Ch

oic

eR

esp

on

se

Octo

ber

Hope

40%

Rayne

20%

Weim

ar

Republic

10%

Larr

y B

lodgett T

rio

30%

Th

e i

nfo

rmati

on

an

d c

on

clu

sio

n a

pp

ear

to b

e v

alid

.

Th

e i

nfo

rmati

on

may n

ot

be v

alid

, b

ecau

se t

ho

se s

am

ple

d m

ay n

ot

live

or

vo

te i

n t

he s

tate

rep

resen

tati

ve’s

dis

tric

t. T

he c

on

clu

sio

n m

ay n

ot

be

valid

—w

hile t

he d

ata

su

gg

est

that

tho

se s

urv

eyed

believe s

he i

s d

oin

g a

g

oo

d j

ob

, th

is d

oes n

ot

necessari

ly m

ean

th

e p

eo

ple

will

vo

te f

or

her.

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-2

Ch

ap

ter

12

13

Gle

ncoe A

lgeb

ra 1

12-2

Wh

ich

mea

su

re o

f cen

tra

l te

nd

en

cy

best

rep

resen

ts t

he d

ata

? J

usti

fy y

ou

r a

nsw

er.

Th

en

fin

d t

he m

ea

su

re.

1. SN

OW

FA

LL A

weath

er

stati

on

keep

s re

cord

s of

how

man

y i

nch

es

of

snow

fall

each

week

: {9

, 2,

0,

3,

0,

2,

1,

2,

3,

1}.

2. SA

LES

A

su

perm

ark

et

keep

s re

cord

s of

how

man

y b

oxes

of

cere

al

are

sold

each

day i

n a

week

: {1

2,

9,

11,

14,

19,

49,

18}.

3. ELEC

TIO

NS

A

cit

y c

ou

nci

lman

keep

s tr

ack

of

the n

um

ber

of

vote

s h

e r

ece

ives

in e

ach

dis

tric

t: {

68,

66,

58,

59,

61,

62,

67}.

Giv

en

th

e f

oll

ow

ing

po

rti

on

of

a s

urv

ey

rep

ort,

ev

alu

ate

th

e v

ali

dit

y o

f th

e

info

rm

ati

on

an

d c

on

clu

sio

n.

4. EC

ON

OM

Y T

he G

all

up

poll

ing c

om

pan

y i

nte

rvie

wed

1464 U

.S.

ad

ult

s n

ati

on

wid

e.

Q

uest

ion

: H

ow

wou

ld y

ou

rate

eco

nom

ic c

on

dit

ion

s in

th

is c

ou

ntr

y t

od

ay?

R

esu

lts:

exce

llen

t, 3

%;

good

, 22%

; on

ly f

air

, 44%

; p

oor

32%

C

on

clu

sion

: A

meri

can

s h

ave c

on

fid

en

ce i

n t

he e

con

om

y.

5. D

OG

S A

pet

store

su

rveyed

its

cu

stom

ers

to f

ind

th

eir

favori

te b

reed

of

dog.

Q

uest

ion

: W

hat

is y

ou

r fa

vori

te b

reed

of

dog?

R

esu

lts:

gold

en

retr

iever,

26%

; co

llie

, 19%

; te

rrie

r, 1

1%

; bu

lld

og,

8%

; p

ug,

24%

; oth

er,

12%

C

on

clu

sion

: T

he g

old

en

retr

iever

is t

he f

avori

te d

og o

f m

ost

cu

stom

ers

.

Dete

rm

ine w

heth

er e

ach

dis

pla

y g

ives a

n a

ccu

ra

te p

ictu

re o

f th

e s

urv

ey

resu

lts.

6. TR

ASH

IN

CIN

ER

ATO

RS

A

loca

l n

ew

spap

er

surv

eyed

530 r

an

dom

ly c

hose

n E

ast

wic

h r

esi

den

ts.

Q

uest

ion

: D

o y

ou

su

pp

ort

clo

sin

g t

he t

rash

in

cin

era

tor

in E

ast

wic

h?

C

on

clu

sion

: E

ast

wic

h r

esi

den

ts o

verw

helm

ingly

su

pp

ort

closi

ng t

he t

rash

in

cin

era

tor.

7. IS

SU

ES

A

tele

vis

ion

sta

tion

in

terv

iew

ed

400 r

an

dom

ly c

hose

n v

ote

rs.

Q

uest

ion

: W

hat

issu

e m

att

ers

most

to y

ou

in c

hoosi

ng a

can

did

ate

to v

ote

for?

C

on

clu

sion

: M

ost

vote

rs d

o n

ot

care

abou

t

the e

nvir

on

men

t.

Sk

ills

Pra

ctic

e

An

aly

zin

g S

urv

ey R

esu

lts

Yes

No

250

300

200 0

350

Inci

ner

ato

r V

ote

Vo

te

r C

on

ce

rn

s

mo

de;

the d

ata

set

has m

an

y r

ep

eate

d n

um

bers

2

med

ian

; th

e d

ata

set

has a

n o

utl

ier;

14

mean

; th

e d

ata

set

has n

o o

utl

ier;

63

T

he i

nfo

rmati

on

is v

alid

, b

ut

the d

ata

do

no

t su

pp

ort

th

e c

on

clu

sio

n—

76%

o

f p

eo

ple

po

lled

rate

th

e e

co

no

my a

s “

on

ly f

air

” o

r “p

oo

r.”

T

he s

urv

ey d

oes n

ot

sta

te h

ow

man

y p

eo

ple

were

su

rveyed

; th

e s

am

ple

siz

e m

ay b

e t

oo

sm

all t

o a

ccu

rate

ly r

ep

resen

t th

e p

op

ula

tio

n.

a

pp

ear

as i

f th

ere

were

tw

ice a

s m

an

y “

Yes” r

esp

on

ses

as “

No

” o

nes,

bu

t th

ere

were

on

ly 3

10 “

Yes” r

esp

on

ses

co

mp

are

d t

o 2

20 f

or

“N

o.”

accu

rate

, b

ut

it d

oes n

ot

necessari

ly

su

pp

ort

th

e c

on

clu

sio

n.

Vo

ters

may

care

ab

ou

t th

e e

nvir

on

men

t, b

ut

care

ab

ou

t an

oth

er

issu

e m

ore

.

Th

e g

rap

h a

pp

ears

Th

e g

rap

h m

akes i

t

Answers (Lesson 12-2)

Page 5: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A6 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

14

Gle

ncoe A

lgeb

ra 1

12-2

Wh

ich

mea

su

re o

f cen

tra

l te

nd

en

cy

best

rep

resen

ts t

he d

ata

? J

usti

fy y

ou

r a

nsw

er.

Th

en

fin

d t

he m

ea

su

re.

1. C

ALC

ULA

TO

RS

Th

e m

ath

dep

art

men

t co

un

ts h

ow m

an

y g

rap

hin

g c

alc

ula

tors

are

in

ea

ch c

lass

room

: {2

0,

19,

20,

20,

18,

19,

20,

18,

19}.

2. B

UD

GETIN

G T

he

Bra

dy f

am

ily k

eep

s tr

ack

of

its

mon

thly

ele

ctri

c bil

ls:

{$134,

$122,

$128,

$127,

$136,

$120,

$129}.

3. A

UTO

MA

TED

TELLER

S A

ban

k k

eep

s tr

ack

of

how

man

y c

ust

omer

s u

se i

ts

AT

M e

ach

hou

r: {

39,

42,

44,

120,

54,

48,

43}.

Giv

en

th

e f

oll

ow

ing

po

rti

on

of

a s

urv

ey

rep

ort,

ev

alu

ate

th

e v

ali

dit

y o

f th

e

info

rm

ati

on

an

d c

on

clu

sio

n.

4. H

OM

EW

OR

K C

hri

s p

olle

d 1

6 o

f h

is f

rien

ds

du

rin

g s

tud

y h

all

.Q

ues

tion

: D

o te

ach

ers

at

Ed

ison

Hig

h S

choo

l ass

ign

too

mu

ch h

omew

ork

?R

esu

lts:

yes

, 94%

; n

o, 6

%C

oncl

usi

on:

Tea

cher

s at

Ed

ison

Hig

h S

choo

l sh

ould

ass

ign

les

s h

omew

ork

.

5. SM

OK

ING

Su

rvey

US

A p

olle

d 5

00 r

an

dom

ly s

elec

ted

ad

ult

s in

Ken

tuck

y.

Qu

esti

on:

Do

you

wan

t to

see

sm

okin

g b

an

ned

fro

m r

esta

ura

nts

, bars

, an

d m

ost

ind

oor

pu

bli

c p

lace

s in

Ken

tuck

y?

Res

ult

s: b

an

ned

, 58%

; all

owed

, 41%

; n

ot s

ure

, 1%

Con

clu

sion

: T

he

Un

ited

Sta

tes

shou

ld b

an

sm

okin

g i

nd

oors

.

Dete

rm

ine w

heth

er t

he d

isp

lay

giv

es a

n a

ccu

ra

te p

ictu

re o

f th

e s

urv

ey

resu

lts.

6. R

ED

EV

ELO

PM

EN

T A

loc

al

new

s bro

ad

cast

co

mm

issi

oned

a p

oll

of 6

00 r

an

dom

ly c

hos

en

Pro

vid

ence

res

iden

ts.

Q

ues

tion

: D

o you

su

pp

ort

or o

pp

ose

the

red

evel

opm

ent

of t

he

wate

rfro

nt?

C

oncl

usi

on:

Pro

vid

ence

res

iden

ts s

up

por

t re

dev

elop

ing

the

wate

rfro

nt.

7. PETS

Ern

esto

too

k a

pol

l of

ran

dom

ly s

elec

ted

stu

den

ts

at

his

hig

h s

choo

l an

d a

sked

th

em h

ow m

an

y p

ets

they

ow

ned

. H

e re

cord

ed t

he

resu

lts

an

d m

ad

e th

e gra

ph

sh

own

at

the

righ

t. W

rite

a v

ali

d c

oncl

usi

on u

sin

g d

ata

to

su

pp

ort

you

r an

swer

.

Pra

ctic

e

An

aly

zin

g S

urv

ey R

esu

lts

60

40

20

0

Tw

o o

r M

ore

One

None

80

100

120

Pet

s

Wa

terfr

on

t R

ed

eve

lop

me

nt

mo

de;

20

mean

; $128

med

ian

; 44

T

he s

am

ple

is n

ot

ran

do

m,

so

th

e r

esu

lts m

ay n

ot

be v

alid

. S

tud

en

ts h

ave

a v

este

d i

nte

rest

in t

he r

esu

lts o

f th

e p

oll a

nd

may b

e b

iased

.

Th

e g

rap

h i

s p

ote

nti

ally m

isle

ad

ing

becau

se

“str

on

gly

op

po

se” a

nd

“str

on

gly

su

pp

ort

are

co

lore

d s

imilarl

y.

Mo

re r

esid

en

ts o

pp

ose

red

evelo

pin

g t

he w

ate

rfro

nt.

An

sw

ers

will

vary

.

T

he i

nfo

rmati

on

ap

pears

valid

. T

he c

on

clu

sio

n m

ay n

ot

be v

alid

becau

se

the p

oll w

as t

aken

on

ly a

mo

ng

peo

ple

liv

ing

in

Ken

tucky.

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-2

Ch

ap

ter

12

15

Gle

ncoe A

lgeb

ra 1

12-2

Wo

rd P

rob

lem

Pra

ctic

e

An

aly

zin

g S

urv

ey R

esu

lts

1.PR

OPER

TY

TA

XES

A l

an

dlo

rd i

s k

eep

ing t

rack

of

wh

at

he

pays

each

m

onth

in

pro

per

ty t

axes

so

he

can

bu

dget

acc

ord

ingly

. F

or t

he

firs

t h

alf

of

the

yea

r,

the

tax b

ills

wer

e $256,

$256,

$274,

$256,

$256,

an

d $

274.

Wh

ich

mea

sure

of

cen

tral

ten

den

cy b

est

rep

rese

nts

th

e d

ata

? Ju

stif

y y

our

an

swer

. T

hen

fin

d

the

mea

sure

.

2.G

AS P

RIC

ES

Qu

inn

ipia

c U

niv

ersi

ty

surv

eyed

1534 r

an

dom

ly c

hos

en

regis

tere

d v

oter

s n

ati

onw

ide

an

d a

sked

th

em,

“As

a r

esu

lt o

f th

e re

cen

t ri

se i

n

gas

pri

ces,

have

you

cu

t back

si

gn

ific

an

tly o

n h

ow m

uch

you

dri

ve?

” A

mon

g t

hos

e w

ho

mak

e le

ss t

han

$30,0

00 a

yea

r, 6

7%

said

th

ey h

ad

cu

t back

on

how

mu

ch t

hey

dri

ve

wh

ile

30%

sa

id t

hey

had

not

. B

ase

d o

n t

his

in

form

ati

on,

a n

ewsp

ap

er m

ad

e th

e co

ncl

usi

on t

hat

“Am

eric

an

s are

cu

ttin

g

back

on

th

eir

dri

vin

g b

ecau

se o

f h

igh

gas

pri

ces.

” E

valu

ate

th

e vali

dit

y o

f th

e in

form

ati

on a

nd

con

clu

sion

.

3.B

OD

YB

UIL

DIN

G A

bod

ybu

ild

er k

eep

s tr

ack

of

how

man

y s

ets

of e

ach

exer

cise

h

e p

erfo

rms

each

day:

{9,

8,

6,

5,

11,

7,

10}.

Wh

ich

mea

sure

of

cen

tral

ten

den

cy

bes

t re

pre

sen

ts t

he

data

? Ju

stif

y y

our

an

swer

. T

hen

fin

d t

he

mea

sure

.

4.TR

AN

SPO

RTA

TIO

N T

he

For

d T

own

ship

S

choo

l B

oard

su

rvey

ed 8

6 r

an

dom

ly

sele

cted

stu

den

ts t

o fi

nd

ou

t h

ow

stu

den

ts g

et t

o sc

hoo

l ea

ch d

ay.

Qu

esti

on:

Wh

at

mod

e of

tra

nsp

orta

tion

d

id y

ou u

se t

o get

to

sch

ool

tod

ay?

Con

clu

sion

: M

ost

stu

den

ts t

ak

e th

e bu

s to

sch

ool

ever

y d

ay.

Dri

ve

Walk

Bu

s

20

30

10 0

40

50

Sch

oo

l T

ran

spo

rtat

ion

a.

Evalu

ate

th

e vali

dit

y o

f th

e in

form

ati

on.

b.

Evalu

ate

th

e vali

dit

y o

f th

e co

ncl

usi

on.

c.

Wri

te a

vali

d c

oncl

usi

on o

f you

r ow

n

usi

ng d

ata

to

sup

por

t you

r an

swer

.

m

od

e;

becau

se t

he d

ata

set

has

man

y r

ep

eate

d n

um

bers

; $256

T

he i

nfo

rmati

on

may n

ot

be v

alid

, b

ecau

se i

t d

oes n

ot

sta

te h

ow

m

an

y o

f th

ose p

olled

make l

ess

than

$30,0

00—

the s

am

ple

siz

e

may b

e t

oo

sm

all.

Th

e c

on

clu

sio

n

may n

ot

be v

alid

eit

her,

becau

se

it t

here

is n

o i

nfo

rmati

on

giv

en

ab

ou

t A

meri

can

s a

s a

wh

ole

.

m

ean

; th

ere

are

no

ou

tlie

rs;

8

Th

e s

am

ple

siz

e m

ay n

ot

be

larg

e e

no

ug

h t

o b

e a

valid

re

pre

sen

tati

on

of

the

po

pu

lati

on

.

Th

e d

ata

in

dic

ate

th

at

mo

re

stu

den

ts e

ith

er

walk

or

dri

ve

each

day t

han

take t

he b

us.

Fu

rth

er,

it

is u

ncle

ar

if t

he

stu

den

ts w

ho

to

ok t

he b

us t

hat

day a

re l

ikely

to

take t

he b

us

every

day.

An

sw

ers

may v

ary

.

Answers (Lesson 12-2)

Page 6: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A7 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

16

Gle

ncoe A

lgeb

ra 1

12-2

Wh

en

con

du

ctin

g a

su

rvey,

it i

s im

port

an

t to

kn

ow

how

acc

ura

te y

ou

r d

ata

are

. Y

ou

can

le

arn

more

abou

t th

e a

ccu

racy

of

a s

urv

ey b

y c

alc

ula

tin

g t

he m

arg

in o

f erro

r,

or

the

maxim

um

sta

tist

ical

am

ou

nt

of

the s

urv

ey’s

un

cert

ain

ty.

Wh

en

calc

ula

tin

g t

he m

arg

in o

f err

or,

you

mu

st f

irst

defi

ne t

he c

on

fid

en

ce l

ev

el.

Th

e

con

fid

en

ce l

evel

tell

s h

ow

acc

ura

te t

he p

erc

en

tages

giv

en

in

th

e p

oll

are

, ass

um

ing t

he o

nly

err

or

pre

sen

t is

sta

tist

ical

err

or

(i.e

., n

o b

ias)

. M

ost

poll

s u

se a

con

fid

en

ce l

evel

of

95%

, m

ean

ing t

hat

there

is

at

least

a 9

5%

cert

ain

ty t

hat

the “

tru

e”

perc

en

tage w

ill

be w

ith

in p

lus

or

min

us

the m

arg

in o

f err

or

of

the p

erc

en

tage g

iven

in

th

e s

urv

ey.

Marg

in o

f E

rror

(90%

confidence level) ≈

1.2

9 −

√ #

n

Marg

in o

f E

rror

(95%

confidence level) ≈

0.9

8 −

√ #

n

Marg

in o

f E

rror

(99%

confidence level) ≈

0.8

2 −

√ #

n

n =

sam

ple

siz

e

Th

e c

alc

ula

tion

s above a

ssu

me t

he s

am

ple

siz

e n

is

sign

ific

an

tly s

mall

er

than

th

e

pop

ula

tion

.

ELEC

TIO

NS

A p

oll

of

300 r

an

do

mly

sele

cte

d r

eg

iste

red

vo

ters s

ho

ws

tha

t th

e i

ncu

mb

en

t m

ay

or o

f N

ew

Ca

stl

e i

s l

ea

din

g h

er o

pp

on

en

t b

y a

52%

to

48%

ma

rg

in.

Fin

d t

he m

arg

in o

f erro

r f

or t

he p

oll

assu

min

g a

95%

co

nfi

den

ce l

ev

el.

M9

5% ≈

0.9

8 −

√ #

n

Marg

in o

f err

or

form

ula

for

the 9

5%

confidence leve

l

M9

5% ≈

0.9

8 −

√ ##

300

n =

300

M9

5% ≈

0.0

57

Sim

plif

y.

Th

e m

arg

in o

f err

or

ass

um

ing a

95%

con

fid

en

ce l

evel

is 0

.057,

or ±

5.7

%.

Th

is m

ean

s th

e

mayor’

s act

ual

sup

port

is

95%

lik

ely

to b

e b

etw

een

46.3

% a

nd

57.7

%.

Exerc

ises

1. TO

LL H

IKES

A

poll

of

600 r

an

dom

ly s

ele

cted

ad

ult

s sh

ow

s th

at

65%

of

those

su

rveyed

are

again

st a

pla

n t

o r

ais

e b

rid

ge t

oll

s. F

ind

th

e p

oll

’s m

arg

in o

f err

or

for

the 9

0%

co

nfi

den

ce l

evel.

2. V

AC

ATIO

NS

A

poll

of

1100 r

an

dom

ly s

ele

cted

ad

ult

s sh

ow

s th

at

34%

of

those

su

rveyed

are

pla

nn

ing t

o v

isit

th

e b

each

th

is s

um

mer.

Fin

d t

he p

oll

’s m

arg

in o

f err

or

for

the 9

9%

co

nfi

den

ce l

evel.

3. PO

LIT

ICS

A

poll

of

765 r

an

dom

ly s

ele

cted

regis

tere

d v

ote

rs s

how

s th

at

47%

of

vote

rs

wil

l vote

to r

e-e

lect

th

e i

ncu

mben

t st

ate

sen

ato

r.

a.

Fin

d t

he m

arg

in o

f err

or

for

the 9

5%

con

fid

en

ce l

evel.

b.

Exp

ress

th

e r

an

ge o

f p

oss

ible

su

pp

ort

for

the s

tate

sen

ato

r as

an

in

equ

ali

ty f

or

the

95%

con

fid

en

ce l

evel.

4. A

bou

t h

ow

man

y p

eop

le w

ou

ld n

eed

to b

e s

urv

eyed

to g

ive a

marg

in o

f err

or

of ±

1%

for

the 9

5%

con

fid

en

ce l

evel?

En

rich

men

t

Marg

in o

f E

rro

r

Exam

ple

± 5

.3%

± 2

.5%

± 3

.5%

43.5

% ≤

x ≤

50.5

%

9604

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-3

Ch

ap

ter

12

17

Gle

ncoe A

lgeb

ra 1

12-3

Statis

tic

s a

nd

Param

eters

A s

tati

sti

c i

s a q

uan

tity

calc

ula

ted

fro

m a

sam

ple

. A

pa

ra

mete

r i

s a c

hara

cteri

stic

of

the p

op

ula

tion

of

a w

hole

. S

tati

stic

s ca

n c

han

ge

from

sam

ple

to s

am

ple

wh

ile p

ara

mete

rs d

o n

ot.

Id

en

tify

th

e s

am

ple

an

d t

he p

op

ula

tio

n f

or e

ach

sit

ua

tio

n.

Th

en

describ

e t

he s

am

ple

sta

tisti

c a

nd

th

e p

op

ula

tio

n p

ara

mete

r.

a

. A

t a

lo

ca

l su

perm

ark

et,

a r

an

do

m s

am

ple

of

50 s

ho

pp

ers i

s s

ele

cte

d.

Th

e m

ed

ian

am

ou

nt

sp

en

t a

t th

e s

up

erm

ark

et

is c

alc

ula

ted

fo

r t

he s

am

ple

.

Sam

ple

: th

e g

rou

p o

f 50 s

hop

pers

Pop

ula

tion

: all

sh

op

pers

at

the s

up

erm

ark

et

Sam

ple

sta

tist

ic:

med

ian

am

ou

nt

spen

t of

cust

om

ers

in

th

e s

am

ple

Pop

ula

tion

para

mete

r: m

ed

ian

am

ou

nt

spen

t at

the s

up

erm

ark

et

b. E

very

20 m

inu

tes a

t a

fu

rn

itu

re f

acto

ry

, a

fin

ish

ed

so

fa i

s p

ull

ed

fro

m t

he

assem

bly

lin

e a

nd

ch

eck

ed

fo

r d

efe

cts

. T

he m

ea

n n

um

ber o

f d

efe

cti

ve s

ofa

s o

f a

da

y’s

sa

mp

le i

s t

hen

ca

lcu

late

d.

Sam

ple

: th

e s

ofa

s ch

eck

ed

for

defe

cts

Pop

ula

tion

: all

sofa

s m

an

ufa

ctu

red

Sam

ple

sta

tist

ic:

mean

nu

mber

of

defe

ctiv

e s

ofa

s in

th

e s

am

ple

Pop

ula

tion

para

mete

r: m

ean

nu

mber

of

defe

ctiv

e s

ofa

s m

an

ufa

ctu

red

Exerc

ises

Iden

tify

th

e s

am

ple

an

d t

he p

op

ula

tio

n f

or e

ach

sit

ua

tio

n.

Th

en

describ

e t

he

sa

mp

le s

tati

sti

c a

nd

th

e p

op

ula

tio

n p

ara

mete

r.

1. W

EA

TH

ER

A

mete

oro

logis

t p

lace

s te

n w

eath

er

stati

on

s in

a c

ou

nty

to m

easu

re r

ain

fall

. T

he m

ed

ian

an

nu

al

rain

fall

is

calc

ula

ted

for

the s

am

ple

.

2. B

OTA

NY

A

sci

en

tist

ran

dom

ly s

ele

cts

20 t

rees

in a

fore

st.

Th

e m

ean

heig

ht

of

the

20 t

rees

is t

hen

calc

ula

ted

.

3. PO

LIT

ICS

A

poli

tica

l re

port

er

ran

dom

ly s

ele

cts

25 c

on

gre

ssio

nal

dis

tric

ts a

cross

th

e

cou

ntr

y.

Th

e m

ean

nu

mber

of

vote

s ca

st i

n t

he 2

5 c

on

gre

ssio

nal

dis

tric

ts i

s ca

lcu

late

d.

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n

Sta

tisti

cs a

nd

Para

mete

rs

Exam

ple

Sam

ple

: th

e 1

0 w

eath

er

sta

tio

ns

Po

pu

lati

on

: all l

ocati

on

s i

n t

he c

ou

nty

Sam

ple

sta

tisti

c:

med

ian

an

nu

al

rain

fall i

n t

he s

am

ple

Po

pu

lati

on

para

mete

r: m

ed

ian

an

nu

al

rain

fall a

cro

ss t

he c

ou

nty

Sam

ple

: th

e 2

0 s

ele

cte

d t

rees

Po

pu

lati

on

: all t

rees i

n t

he f

ore

st

Sam

ple

sta

tisti

c:

mean

heig

ht

of

trees i

n t

he s

am

ple

Po

pu

lati

on

para

mete

r: m

ean

heig

ht

of

trees i

n t

he f

ore

st

Sam

ple

: th

e 2

5 s

ele

cte

d c

on

gre

ssio

nal

dis

tric

tsP

op

ula

tio

n:

all c

on

gre

ssio

nal

dis

tric

ts n

ati

on

wid

eS

am

ple

sta

tisti

c:

mean

nu

mb

er

of

vo

tes c

ast

in t

he s

am

ple

Po

pu

lati

on

para

mete

r: m

ean

nu

mb

er

of

vo

tes c

ast

nati

on

wid

e

Answers (Lesson 12-2 and Lesson 12-3)

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Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A8 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

18

Gle

ncoe A

lgeb

ra 1

12-3

Sta

tist

ical

An

aly

sis

Th

e m

ea

n a

bso

lute

dev

iati

on

is

the a

vera

ge o

f th

e a

bso

lute

valu

es

of

the d

iffe

ren

ces

betw

een

th

e m

ean

an

d e

ach

valu

e i

n t

he d

ata

set.

It

is u

sed

to

pre

dic

t err

ors

an

d j

ud

ge e

qu

ali

ty.

Th

e s

tan

da

rd

dev

iati

on

is

the c

alc

ula

ted

valu

e t

hat

show

s h

ow

data

devia

te f

rom

th

e m

ean

of

the s

et

of

data

. T

he v

aria

nce

of

data

is

the

squ

are

of

the s

tan

dard

devia

tion

.

EM

PLO

YM

EN

T

Em

plo

yees a

t a

la

w f

irm

keep

tra

ck

of

ho

w m

an

y

ho

urs t

hey

wo

rk

ea

ch

week

: {4

4,

48,

44,

40,

59}.

a

. F

ind

th

e m

ea

n a

bso

lute

dev

iati

on

.

Ste

p 1

F

ind

th

e m

ean

. F

or

this

set

of

data

, th

e m

ean

is

47.

Ste

p 2

F

ind

th

e s

um

of

the a

bso

lute

valu

es

of

the d

iffe

ren

ces

betw

een

each

valu

e i

n t

he s

et

of

data

an

d t

he m

ean

.

4

4 -

47 +

48 -

47 +

44 -

47 +

|40 -

47| +

59 -

47 =

3 +

1 +

3 +

7 +

12 =

26

Ste

p 3

D

ivid

e t

he s

um

by t

he n

um

ber

of

valu

es

in t

he s

et

of

data

: 26 ÷

5 ≠

5.2

Th

e m

ean

abso

lute

devia

tion

is

5.2

.

b. F

ind

th

e v

aria

nce a

nd

sta

nd

ard

dev

iati

on

.

Ste

p 1

T

o f

ind

th

e v

ari

an

ce,

squ

are

th

e d

iffe

ren

ce b

etw

een

each

nu

mber

an

d t

he m

ean

. T

hen

div

ide b

y t

he n

um

ber

of

valu

es.

σ2 =

(44 -

47

)2 +

(4

8 -

47)2

+ (

44 -

47

)2 +

(40 -

45)2

+ (

59 -

47

)2

−−−−

5

= (-

3)2

+ (

1)2

+ (-

3)2

+ (-

5)2

+ (

12)2

−−−

5

=

9 +

1 +

9 +

25

+ 1

44

−−

5

=

188

5

Ste

p 2

T

he s

tan

dard

devia

tion

is

the s

qu

are

root

of

the v

ari

an

ce.

&

σ2 =

√ &

&

188

5

σ ≈

6.1

3

Th

e v

ari

an

ce o

f th

e d

ata

set

is 1

88

5

an

d t

he s

tan

dard

devia

tion

is

ap

pro

xim

ate

ly 6

.13.

Exerc

ises

Fin

d t

he m

ea

n,

mea

n a

bso

lute

dev

iati

on

, v

aria

nce,

an

d s

tan

da

rd

dev

iati

on

fo

r

ea

ch

set

of

da

ta.

1. {2

, 4,

9,

5}

2. {1

3,

17,

17,

22,

16}

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n (continued)

Sta

tisti

cs a

nd

Param

ete

rs

Exam

ple

x = 5

; m

ean

ab

so

lute

devia

tio

n =

2;

σ2 =

5.2

; σ ≈ 2

.28

− x = 1

7;

mean

ab

so

lute

devia

tio

n =

2;

σ2 =

8.4

; σ ≈ 2

.90

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-3

12-3

Iden

tify

th

e s

am

ple

an

d t

he p

op

ula

tio

n f

or e

ach

sit

ua

tio

n.

Th

en

describ

e t

he

sa

mp

le s

tati

sti

c a

nd

th

e p

op

ula

tio

n p

ara

mete

r.

1. R

ESTA

UR

AN

TS

A

rest

au

ran

t ra

nd

om

ly s

ele

cts

10 p

atr

on

s on

Satu

rday n

igh

t. T

he

med

ian

am

ou

nt

spen

t on

bevera

ges

is t

hen

calc

ula

ted

for

the s

am

ple

.

2. K

ITTEN

S A

vete

rin

ari

an

ran

dom

ly s

ele

cts

3 k

itte

ns

from

a l

itte

r. T

he m

ean

weig

ht

of

the 3

kit

ten

s is

calc

ula

ted

.

3. PR

OD

UC

E A

pro

du

ce c

lerk

ran

dom

ly s

ele

cts

20 b

ags

of

ap

ple

s fr

om

each

week

’s

ship

men

t an

d c

ou

nts

th

e t

ota

l n

um

ber

of

ap

ple

s in

each

bag.

Th

e m

od

e n

um

ber

of

ap

ple

s is

calc

ula

ted

for

the s

am

ple

.

Fin

d t

he m

ea

n a

bso

lute

dev

iati

on

.

4. W

ILD

LIF

E A

rese

arc

her

cou

nts

th

e n

um

ber

of

river

ott

ers

obse

rved

on

each

acr

e

of

lan

d i

n a

sta

te p

ark

: {0

, 10,

14,

6,

0,

8,

4}.

4

5. FIS

HIN

G A

fis

herm

an

reco

rds

the w

eig

ht

of

each

bla

ck b

ass

he c

atc

hes

du

rin

g

a f

ish

ing t

rip

: {1

2,

7,

8,

13,

6,

14}.

3

6. B

UD

GETIN

G X

avie

r k

eep

s tr

ack

of

how

mu

ch m

on

ey h

e s

pen

ds

on

gaso

lin

e

each

week

: {2

0,

13,

26,

0,

33,

16,

18}.

Fin

d t

he m

ea

n,

va

ria

nce,

an

d s

tan

da

rd

dev

iati

on

of

ea

ch

set

of

da

ta.

7. {2

, 0,

10,

4}

8. {6

, 7,

6,

9}

9. {1

0,

9,

13,

6,

7}

10. {6

, 8,

2,

3,

2,

9}

11. {2

3,

18,

28,

26,

15}

12. {4

4,

35,

50,

37,

43,

38,

40}

13. PA

RK

ING

A

cit

y c

ou

nci

lor

wan

ts t

o k

now

how

mu

ch r

even

ue t

he c

ity w

ou

ld e

arn

by

inst

all

ing p

ark

ing m

ete

rs o

n M

ain

Str

eet.

He c

ou

nts

th

e n

um

ber

of

cars

park

ed

on

Main

Str

eet

each

week

day:

{64,

79,

81,

53,

63}.

Fin

d t

he s

tan

dard

devia

tion

. 10.5

5

Ch

ap

ter

12

19

Gle

ncoe A

lgeb

ra 1

Sk

ills

Pra

ctic

e

Sta

tisti

cs a

nd

Param

ete

rs

x =

4; σ

2 =

14; σ ≈ 3

.74

x =

7; σ

2 =

1.5

; σ ≈ 1

.22

x =

5; σ

2 =

8

3 ; σ ≈

1.6

3 −

x =

9; σ

2 =

6; σ ≈ 2

.45

x =

41; σ

2 =

156

7

; σ ≈ 4

.72

x =

22; σ

2 =

23.6

; σ ≈ 4

.86

Sam

ple

: th

e 1

0 s

ele

cte

d p

atr

on

s

Po

pu

lati

on

: all p

atr

on

s o

n S

atu

rday n

igh

t

Sam

ple

sta

tisti

c:

med

ian

am

ou

nt

sp

en

t o

n b

evera

ges i

n t

he s

am

ple

Po

pu

lati

on

para

mete

r: m

ed

ian

am

ou

nt

sp

en

t o

n b

evera

ges o

n S

atu

rday n

igh

t

Sam

ple

: th

e 3

sele

cte

d k

itte

ns

Po

pu

lati

on

: all k

itte

ns i

n t

he l

itte

r

Sam

ple

sta

tisti

c:

the m

ean

weig

ht

of

the k

itte

ns i

n t

he s

am

ple

Po

pu

lati

on

para

mete

r: t

he m

ean

weig

ht

of

the k

itte

ns i

n t

he l

itte

r

Sam

ple

: th

e 2

0 s

ele

cte

d b

ag

s o

f ap

ple

s

Po

pu

lati

on

: all b

ag

s o

f ap

ple

s i

n t

he w

eek’s

sh

ipm

en

t

Sam

ple

sta

tisti

c:

mo

de n

um

ber

of

ap

ple

s i

n t

he s

am

ple

Po

pu

lati

on

para

mete

r: m

od

e n

um

ber

of

ap

ple

s i

n t

he w

eek’s

sh

ipm

en

t

5

0

7

Answers (Lesson 12-3)

Page 8: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A9 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

20

Gle

ncoe A

lgeb

ra 1

12-3

Iden

tify

th

e s

am

ple

an

d t

he p

op

ula

tio

n f

or e

ach

sit

ua

tio

n.

Th

en

describ

e t

he

sa

mp

le s

tati

sti

c a

nd

th

e p

op

ula

tio

n p

ara

mete

r.

1. M

AR

INE B

IOLO

GY

A

mari

ne b

iolo

gis

t ra

nd

om

ly s

ele

cts

30 o

yst

ers

fro

m a

rese

arc

h

tan

k.

Th

e m

ean

weig

ht

of

the 3

0 o

yst

ers

is

calc

ula

ted

.

2. C

IVIL

EN

GIN

EER

ING

A

civ

ic e

ngin

eer

ran

dom

ly s

ele

cts

5 c

ity i

nte

rsect

ion

s w

ith

tra

ffic

ligh

ts.

Th

e m

ed

ian

len

gth

of

a r

ed

lig

ht

is c

alc

ula

ted

for

the s

am

ple

.

3. B

ASEB

ALL A

base

ball

com

mis

sion

er

ran

dom

ly s

ele

cts

10 h

om

e g

am

es

pla

yed

by a

majo

r le

agu

e t

eam

. T

he m

ed

ian

att

en

dan

ce i

s ca

lcu

late

d f

or

the g

am

es

in t

he s

am

ple

.

Fin

d t

he m

ea

n a

bso

lute

dev

iati

on

.

4. IN

VESTIN

G A

sto

ck b

rok

er

keep

s a r

eco

rd o

f th

e d

ail

y c

losi

ng p

rice

of

a s

hare

of

stock

in B

icso

mm

Corp

ora

tion

: {4

5.2

0,

46.1

0,

46.8

5,

42.5

5,

40.8

0}.

2.1

0

5. G

OLF A

golf

er

keep

s tr

ack

of

his

sco

res

for

each

rou

nd

: {7

8,

81,

86,

77,

75}.

3.2

8

6. W

EA

TH

ER

A

mete

oro

logis

t k

eep

s tr

ack

of

the n

um

ber

of

thu

nd

ers

torm

s occ

uri

ng e

ach

mon

th i

n S

uss

ex C

ou

nty

: {0

, 4,

7,

1,

3,

5,

2}.

ap

pro

xim

ate

ly 1

.88

Fin

d t

he m

ea

n,

va

ria

nce,

an

d s

tan

da

rd

dev

iati

on

of

ea

ch

set

of

da

ta.

7. {6

, 11,

16,

9}

8. {2

, 5,

8,

11,

4}

9. {2

3.4

, 16.8

, 9.7

, 22.1

} 10. {1

, 5

2 ,

4,

11

2 ,

1

2 ,

3}

11. {1

45,

166,

171,

150,

88}

12. {1

3,

24,

22,

17,

14,

29,

15,

22}

13. Q

UA

LIT

Y C

ON

TR

OL A

n i

nsp

ect

or

check

s each

au

tom

obil

e t

hat

com

es

off

of

the

ass

em

bly

lin

e.

He k

eep

s a r

eco

rd o

f th

e n

um

ber

of

defe

ctiv

e c

ars

each

day:

{3,

1,

2,

0,

0,

4,

3,

6,

1,

2}.

Fin

d t

he s

tan

dard

devia

tion

. ap

pro

xim

ate

ly 1

.78

Practi

ce

Sta

tisti

cs a

nd

Param

ete

rs

Sam

ple

: th

e 3

0 s

ele

cte

d o

yste

rsP

op

ula

tio

n:

all o

yste

rs i

n t

he r

esearc

h t

an

kS

am

ple

sta

tisti

c:

mean

weig

ht

of

oyste

rs i

n t

he s

am

ple

Po

pu

lati

on

para

mete

r: m

ean

weig

ht

of

oyste

rs i

n t

he r

esearc

h t

an

k

Sam

ple

: th

e 5

cit

y i

nte

rsecti

on

s w

ith

tra

ffic

lig

hts

Po

pu

lati

on

: all c

ity i

nte

rsecti

on

s w

ith

tra

ffic

lig

hts

Sam

ple

sta

tisti

c:

the m

ed

ian

len

gth

of

a r

ed

lig

ht

in t

he s

am

ple

Po

pu

lati

on

para

mete

r: t

he m

ed

ian

len

gth

of

a r

ed

lig

ht

at

all c

ity i

nte

rsecti

on

s

Sam

ple

: th

e 1

0 s

ele

cte

d h

om

e g

am

es p

layed

by t

he t

eam

Po

pu

lati

on

: all h

om

e g

am

es p

layed

by t

he t

eam

Sam

ple

sta

tisti

c:

med

ian

att

en

dan

ce f

or

the g

am

es i

n t

he s

am

ple

Po

pu

lati

on

para

mete

r: m

ed

ian

att

en

dan

ce f

or

all t

he h

om

e g

am

es p

layed

by

the t

eam

x =

10.5

; σ

2 =

53

4 ;

σ ≈ 3

.64

x =

6; σ

2 =

10; σ ≈ 3

.16

x =

18; σ

2 =

29.0

75; σ ≈ 5

.39

x =

11

4 ;

σ2 =

139

48 ;

σ ≈ 1

.70

x =

19.5

; σ

2 =

27.7

5; σ ≈ 5

.27

x =

144; σ

2 =

877.2

; σ ≈ 2

9.6

2

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-3

Ch

ap

ter

12

21

Gle

ncoe A

lgeb

ra 1

12-3

1. G

AS P

RIC

ES

R

en

ee i

s p

lan

nin

g a

road

trip

to h

er

au

nt’

s h

ou

se.

To e

stim

ate

how

mu

ch t

he t

rip

wil

l co

st,

she g

oes

on

lin

e

an

d f

ind

s th

e p

rice

of

a g

all

on

of

gaso

lin

e

for

5 r

an

dom

ly s

ele

cted

gas

stati

on

s

alo

ng t

he r

ou

te.

Sh

e t

hen

calc

ula

tes

the

med

ian

pri

ce p

er

gall

on

for

the 5

sele

cted

gas

stati

on

s.

a.

Iden

tify

th

e s

am

ple

an

d t

he

pop

ula

tion

.

b.

Desc

ribe t

he s

am

ple

sta

tist

ic a

nd

th

e

pop

ula

tion

para

mete

r.

2. SU

MM

ER

VA

CA

TIO

N M

r. S

iip

ola

’s

alg

ebra

cla

ss t

ook

a s

urv

ey t

o f

ind

stu

den

ts’ p

lan

s fo

r th

e s

um

mer.

Th

e

resu

lts

are

sh

ow

n i

n t

he c

ircl

e g

rap

h.

Su

mm

er P

lan

s

Fin

d t

he m

ean

abso

lute

vari

ati

on

for

the

poll

resu

lts.

16.4

3. H

OC

KEY

A

hock

ey t

eam

keep

s tr

ack

of

how

man

y g

oals

it

score

s each

gam

e:

{2,

4,

0,

3,

7,

2}.

Fin

d t

he m

ean

, vari

an

ce,

an

d s

tan

dard

devia

tion

of

the d

ata

.

x=

3, σ

2=

14

− 3, σ ≈ 2

.16

4. ER

RO

R A

NA

LY

SIS

M

yau

an

d A

lice

are

stu

dyin

g f

or

their

test

on

sta

tist

ics.

Myau

hyp

oth

esi

zes

that

the v

ari

an

ce o

f a s

et

of

data

wil

l alw

ays

be a

gre

ate

r n

um

ber

than

th

e s

tan

dard

devia

tion

. A

lice

beli

eves

that

Myau

is

inco

rrect

an

d t

hat

the s

tan

dard

vari

ati

on

can

be a

gre

ate

r

nu

mber

than

th

e v

ari

an

ce.

Wh

o i

s

corr

ect

? E

xp

lain

.

5. H

EA

LTH

CLU

BS

T

o p

lan

th

eir

fu

ture

equ

ipm

en

t p

urc

hase

s, t

he N

ort

hvil

le

Healt

h C

lub r

an

dom

ly c

hoose

s 8 p

atr

on

s

an

d t

rack

s h

ow

man

y m

inu

tes

they

spen

d o

n t

he t

read

mil

l: {

30,

30,

45,

20,

60,

30,

30,

15}.

Th

e m

ean

tre

ad

mil

l ti

me

is t

hen

calc

ula

ted

.

a.

Iden

tify

th

e s

am

ple

an

d t

he

pop

ula

tion

. T

hen

desc

ribe t

he s

am

ple

stati

stic

an

d t

he p

op

ula

tion

para

mete

r.

b.

Fin

d t

he s

am

ple

sta

tist

ic s

peci

fied

in

part

a.

32.5

min

ute

s

c.

Fin

d t

he m

ean

abso

lute

devia

tion

for

the s

am

ple

. 10

d.

Fin

d t

he v

ari

an

ce a

nd

sta

nd

ard

devia

tion

for

the s

am

ple

. σ

2=

175;

σ≈

13.2

3

Wo

rd

Pro

ble

m P

racti

ce

Sta

tisti

cs a

nd

Param

ete

rs

Sam

ple

: th

e 5

sele

cte

d g

as s

tati

on

sP

op

ula

tio

n:

all g

as s

tati

on

s a

lon

g

the r

ou

te

Sam

ple

sta

tisti

c:

med

ian

pri

ce p

er

gallo

n o

f g

aso

lin

e i

n t

he s

am

ple

Po

pu

lati

on

para

mete

r: m

ed

ian

p

rice p

er

gallo

n o

f g

aso

lin

e a

lon

g

the r

ou

te

Alice i

s c

orr

ect.

Sam

ple

an

sw

er:

Th

e

sta

nd

ard

devia

tio

n w

ill

be g

reate

r th

an

th

e v

ari

an

ce f

or

clo

sely

rela

ted

d

ata

. F

or

exam

ple

, th

e v

ari

an

ce o

f th

e d

ata

set

{5,

5,

5,

5,

6}

is 0

.232;

the s

tan

dard

devia

tio

n i

s

ap

pro

xim

ate

ly 0

.482.

Sam

ple

: th

e 8

sele

cte

d p

atr

on

sP

op

ula

tio

n:

all p

atr

on

s u

sin

g t

he

tread

mill

Sam

ple

sta

tisti

c:

mean

tim

e o

n

the t

read

mill

for

the s

am

ple

Po

pu

lati

on

para

mete

r: m

ean

tim

e

on

th

e t

read

mill

for

all p

atr

on

s

wh

o u

se i

t

Answers (Lesson 12-3)

Page 9: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A10 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

22

Gle

ncoe A

lgeb

ra 1

12-3

You

ju

st l

earn

ed

abou

t st

an

dard

devia

tion

, w

hic

h m

easu

res

how

wid

ely

sp

read

data

poin

ts

in a

sam

ple

are

—ess

en

tiall

y,

how

far

data

poin

ts a

re f

rom

th

e m

ean

.

An

oth

er

key s

tati

stic

al

measu

re i

s th

e s

tan

da

rd

erro

r o

f th

e m

ea

n,

or

SE.

Th

e s

tan

dard

err

or

of

the m

ean

desc

ribes

the u

nce

rtain

ty o

f h

ow

th

e s

am

ple

mean

rep

rese

nts

th

e

pop

ula

tion

mean

, an

d i

s giv

en

by t

he e

qu

ati

on

SE =

σ −

√ $

n ,

wh

ere

σ i

s th

e s

tan

dard

devia

tion

an

d n

is

the s

am

ple

siz

e.

Th

e e

qu

ati

on

for

the s

tan

dard

err

or

ind

icate

s th

at

the l

arg

er

the s

am

ple

siz

e i

s, t

he s

mall

er

the s

tan

dard

err

or

wil

l be.

Th

e s

tan

dard

err

or

is o

ften

desc

ribed

in

term

s of

perc

en

tages

call

ed

co

nfi

den

ce l

imit

s. 95%

con

fid

en

ce l

imit

in

terv

al =

x ± 1

.96

SE

99%

con

fid

en

ce l

imit

in

terv

al =

x ± 2

.58

SE

T

he s

tan

da

rd

dev

iati

on

of

the w

eig

ht

of

ind

ivid

ua

l a

pp

les a

t M

r.

Ma

gu

ire’s

sta

nd

is 0

.8 o

un

ces.

Th

e m

ea

n w

eig

ht

of

a s

am

ple

of

25 a

pp

les i

s

5.2

ou

nces.

Fin

d t

he 9

9%

co

nfi

den

ce i

nte

rv

al

for t

he m

ea

n.

Fir

st,

calc

ula

te t

he s

tan

dard

err

or.

SE =

σ −

√ $

n =

0.8 −

√ $$

25 =

0.1

6

Th

en

, u

se t

he e

qu

ati

on

above f

or

the 9

9%

con

fid

en

ce i

nte

rval.

99%

con

fid

en

ce i

nte

rval = −

x ± 2

.58

SE

= 5

.2 ± 2

.58(0

.16) =

5.2

± 0

.4128

Th

e 9

9%

con

fid

en

ce i

nte

rval

is 4

.7872 t

o 5

.6128.

Th

is m

ean

s w

e c

an

be 9

9%

su

re t

hat

the

pop

ula

tion

mean

is

betw

een

4.7

872 a

nd

5.6

128.

Exerc

ises

Fin

d t

he s

tan

da

rd

erro

r o

f th

e m

ea

n f

or e

ach

da

ta s

et.

1. {3

06,

313,

301,

293,

326,

315}

2. {0

.50,

0.4

3,

0.2

7,

0.6

4,

0.6

2,

0.6

0}

≈ 4

.31

0.5

3

3. C

HEESE

T

he l

oca

l su

perm

ark

et

pack

ages

fresh

ch

eese

in

refr

igera

ted

case

s fo

r it

s cu

stom

ers

’ co

nven

ien

ce.

Th

e w

eig

hts

of

the p

ack

ages

of

parm

esa

n c

urr

en

tly i

n t

he c

ase

, in

ou

nce

s, a

re:

{14,

12,

16,

17,

12,

16,

14,

19,

15}.

a.

Fin

d t

he s

tan

dard

err

or

for

the m

ean

for

the d

ata

set.

0.7

2

b.

Fin

d t

he 9

5%

con

fid

en

ce i

nte

rval

for

the m

ean

. ≈

13.5

9 t

o ≈

16.4

1

4. C

HIL

D C

AR

E T

he s

tan

dard

devia

tion

of

the a

ges

of

the c

hil

dre

n a

t th

e H

ap

py S

mil

es

Ch

ild

Care

Cen

ter

is 1

.2 y

ears

. T

he m

ean

age o

f a s

am

ple

of

9 c

hil

dre

n w

as

7.4

years

.

a.

Fin

d t

he 9

5%

con

fid

en

ce i

nte

rval

for

the m

ean

. 6.6

16 t

o 8

.184

b.

How

man

y c

hil

dre

n m

ust

be i

ncl

ud

ed

in

th

e s

am

ple

to b

e 9

5%

cert

ain

th

at

the

est

imate

of

the m

ean

has

an

err

or

of

plu

s or

min

us

0.5

years

?

En

rich

men

t

Sta

nd

ard

Erro

r a

nd

Co

nfi

den

ce L

imit

s

Exam

ple

at

least

23 c

hild

ren

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-4

Ch

ap

ter

12

23

Gle

ncoe A

lgeb

ra 1

12-4

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n

Perm

uta

tio

ns a

nd

Co

mb

inati

on

s

Perm

utatio

ns

An

arr

an

gem

en

t or

list

ing i

n w

hic

h o

rder

or

pla

cem

en

t is

im

port

an

t is

ca

lled

a p

erm

uta

tio

n.

For

exam

ple

, th

e a

rran

gem

en

t A

B o

f ch

oic

es

A a

nd

B i

s d

iffe

ren

t fr

om

th

e a

rran

gem

en

t B

A o

f th

ese

sam

e t

wo c

hoic

es.

Perm

uta

tio

ns

P(n

, r) =

n! −

(n - r

)!

F

ind

P(6

, 2).

P(n

, r)

=

n! −

(n -

r)!

Definitio

n o

f p

(n,

r)

P(6

, 2) =

6! −

(6 -

2)!

n =

6,

r =

2

= 6

! −

4!

S

implif

y.

= 6

· 5

· 4

· 3

· 2

· 1

−−

4 ·

3 ·

2 ·

1

D

efinitio

n o

f fa

cto

rial

=

6 ·

5 o

r 30

Sim

plif

y.

Th

ere

are

30 p

erm

uta

tion

s of

6 o

bje

cts

tak

en

2 a

t a t

ime.

PA

SSW

OR

DS

A s

pecif

ic p

ro

gra

m r

eq

uir

es t

he u

ser t

o e

nte

r a

5-d

igit

pa

ssw

ord

. T

he d

igit

s c

an

no

t rep

ea

t a

nd

ca

n b

e a

ny

fiv

e o

f th

e d

igit

s

1,

2,

3,

4,

7,

8,

an

d 9

.

a.

Ho

w m

an

y d

iffe

ren

t p

assw

ord

s a

re p

ossib

le?

P

(n,

r) =

n! −

(n -

r)!

P

(7,

5) =

7! −

(7 -

5)!

=

7 ·

6 ·

5 ·

4 ·

3 ·

2 ·

1

−−

2 ·

1

=

7 ·

6 ·

5 ·

4 ·

3 o

r 2520

Th

ere

are

2520 w

ays

to c

reate

a p

ass

word

.

b.

Wh

at

is t

he p

ro

ba

bil

ity

th

at

the f

irst

two

dig

its

are o

dd

nu

mb

ers w

ith

th

e o

ther d

igit

s a

ny

of

the r

em

ain

ing

nu

mb

ers?

P

(fir

st t

wo d

igit

s od

d) =

nu

mber

of

favora

ble

ou

tcom

es

−−

nu

mber

of

poss

ible

ou

tcom

es

S

ince

th

ere

are

4 o

dd

dig

its,

th

e n

um

ber

of

choic

es

for

the f

irst

dig

it i

s 4,

an

d t

he n

um

ber

of

choic

es

for

the s

eco

nd

dig

it i

s 3.

Th

en

th

ere

are

5 c

hoic

es

left

for

the t

hir

d d

igit

, 4 f

or

the f

ou

rth

, an

d 3

for

the f

ifth

, so

th

e n

um

ber

of

favora

ble

ou

tcom

es

is 4

· 3

· 5

· 4

· 3

, or

720.

T

he p

robabil

ity i

s 7

20 −

2520 ≈

28.6

%.

Exerc

ises

Ev

alu

ate

ea

ch

ex

pressio

n.

1.

P(7

, 4)

2. P

(12,

7)

3. [P

(9,

9)]

[P(1

6,

2)]

840

3,9

91,6

80

87,0

91,2

00

4. C

LU

BS

A

clu

b w

ith

ten

mem

bers

wan

ts t

o c

hoose

a p

resi

den

t, v

ice-p

resi

den

t, s

ecr

eta

ry,

an

d t

reasu

rer.

Six

of

the m

em

bers

are

wom

en

, an

d f

ou

r are

men

.

a

. H

ow

man

y d

iffe

ren

t se

ts o

f off

icers

are

poss

ible

? 5040

b

. W

hat

is t

he p

robabil

ity t

hat

all

off

icers

wil

l be w

om

en

. 7.1

%

Exam

ple

1

Exam

ple

2

Answers (Lesson 12-3 and Lesson 12-4)

Page 10: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A11 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

24

Gle

ncoe A

lgeb

ra 1

12-4

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n (c

on

tin

ued

)

Perm

uta

tio

ns a

nd

Co

mb

inati

on

s

Co

mb

inatio

ns

An

arr

an

gem

en

t or

list

ing i

n w

hic

h o

rder

is n

ot

imp

ort

an

t is

call

ed

a

com

bin

ati

on

. F

or

exam

ple

, A

B a

nd

BA

are

th

e s

am

e c

om

bin

ati

on

of

A a

nd

B.

Co

mb

inati

on

sC

(n,

r) =

n! −

(n -

r)!

r!

A

clu

b w

ith

ten

mem

bers w

an

ts t

o c

ho

ose a

co

mm

itte

e o

f fo

ur

mem

bers.

Six

of

the m

em

bers a

re w

om

en

, a

nd

fo

ur a

re m

en

.

a.

Ho

w m

an

y d

iffe

ren

t co

mm

itte

es a

re p

ossib

le?

C

(n,

r) =

n

! −

(n -

r)!

r!

Definitio

n o

f com

bin

ation

=

10! −

(10 -

4)!

4!

n =

10,

r =

4

= 1

0 ·

9 ·

8 ·

7 −

4!

D

ivid

e b

y t

he G

CF

6!.

=

210

Sim

plif

y.

T

here

are

210 w

ays

to c

hoose

a c

om

mit

tee o

f fo

ur

wh

en

ord

er

is n

ot

imp

ort

an

t.

b.

If t

he c

om

mit

tee i

s c

ho

sen

ra

nd

om

ly,

wh

at

is t

he p

ro

ba

bil

ity

th

at

two

mem

bers

of

the c

om

mit

tee a

re m

en

?

T

here

are

C(4

, 2)

4! −

(4 -

2)!

2! =

6 w

ays

to c

hoose

tw

o m

en

ran

dom

ly,

an

d t

here

are

C

(6,

2) =

6! −

(6 -

4)!

4! =

15 w

ays

to c

hoose

tw

o w

om

en

ran

dom

ly.

By t

he F

un

dam

en

tal

Cou

nti

ng P

rin

cip

le,

there

are

6 ·

15 o

r 90 w

ays

to c

hoose

a c

om

mit

tee w

ith

tw

o m

en

an

d

two w

om

en

.

Pro

babil

ity (

2 m

en

an

d 2

wom

en

) = n

um

ber

of

favora

ble

ou

tcom

es

−−

nu

mber

of

poss

ible

ou

tcom

es

= 9

0 −

210 o

r abou

t 42.9

%

Exerc

ises

Ev

alu

ate

ea

ch

ex

pressio

n.

1.

C(7

, 3)

35

2. C

(12,

8)

495

3. C

(9,

9)

1

4. C

OM

MIT

TEES

In

how

man

y w

ays

can

a c

lub w

ith

9 m

em

bers

ch

oose

a t

wo-m

em

ber

sub-c

om

mit

tee?

36

5. B

OO

K C

LU

BS

A

book

clu

b o

ffers

its

mem

bers

a b

ook

each

mon

th f

or

a y

ear

from

a

sele

ctio

n o

f 24 b

ook

s. T

en

of

the b

ook

s are

bio

gra

ph

ies

an

d 1

4 o

f th

e b

ook

s are

fic

tion

.

a.

How

man

y w

ays

cou

ld t

he m

em

bers

sele

ct 1

2 b

ook

s? 2,7

04,1

56

b.

Wh

at

is t

he p

robabil

ity t

hat

5 b

iogra

ph

ies

an

d 7

fic

tion

book

s w

ill

be c

hose

n?

ab

ou

t 32%

Exam

ple

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-4

Ch

ap

ter

12

25

Gle

ncoe A

lgeb

ra 1

12-4

Sk

ills

Pra

ctic

e

Perm

uta

tio

ns a

nd

Co

mb

inati

on

s

Use t

he F

un

da

men

tal

Co

un

tin

g P

rin

cip

le t

o e

va

lua

te e

ach

of

the f

oll

ow

ing

.

1. SC

HO

OL P

LA

Y Jose

ph

an

d e

igh

t fr

ien

ds

are

att

en

din

g t

he s

chool

pla

y.

How

man

y

ways

can

Jose

ph

an

d h

is f

rien

ds

sit

in 9

em

pty

seats

? 362,8

80

2. V

IDEO

S S

an

jay i

s arr

an

gin

g h

is 6

favori

te v

ideos

on

a s

helf

. In

how

man

y w

ays

can

he d

o t

his

? 720

Ev

alu

ate

ea

ch

ex

pressio

n.

3.

P(5

, 2)

20

4. P

(6,

4)

360

5. P

(7,

3)

210

6.

P(9

, 4)

3024

7. P

(7,

5)

2520

8. P

(5,

3)

60

9.

C(6

, 2)

15

10. C

(9,

7)

36

11. C

(8,

4)

70

12. C

(7,

5)

21

13. C

(12,

2)

66

14. C

(13,

7)

1716

15. C

(11,

2)

55

16. P

(5,

4)

120

17. C

(14,

5)

2002

18. C

(11,

6)

462

19. P

(4,

2)

12

20. C

(8,

6)

28

Answers (Lesson 12-4)

Page 11: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A12 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

26

Gle

ncoe A

lgeb

ra 1

12-4

Practi

ce

Perm

uta

tio

ns a

nd

Co

mb

inati

on

s

Use t

he F

un

da

men

tal

Co

un

tin

g P

rin

cip

le t

o e

va

lua

te e

ach

of

the f

oll

ow

ing

.

1. ER

RA

ND

S W

esl

ey n

eed

s to

sto

p a

t 6 s

tore

s on

th

e w

ay h

om

e f

rom

work

. H

ow

man

y

ways

can

Wesl

ey a

rran

ge t

he 6

sto

ps

he n

eed

s to

mak

e?

720

2. V

OTIN

G T

here

are

8 p

eop

le w

ait

ing i

n l

ine t

o c

ast

th

eir

vote

s. H

ow

man

y w

ays

can

th

e

pep

ole

lin

e u

p t

o v

ote

? 40,3

20

Ev

alu

ate

ea

ch

ex

pressio

n.

3. P

(11,

3)

990

4. P

(6,

3)

120

5. P

(15,

3)

2730

6. C

(10,

9)

10

7. C

(12,

9)

220

8. C

(7,

3)

35

9. C

(7,

4)

35

10. C

(12,

4)

495

11. P

(13,

3)

1716

12. C

(16,

12)

1820

13. C

(17,

2)

136

14. C

(16,

15)

16

15. P

(20,

5)

1,8

60,4

80

16. P

(11,

7)

1,6

63,2

00

17. P

(13,

1)

13

18. C

(19,

16)

969

19. P

(15,

4)

32,7

60

20. C

(14,

7)

3432

21. SPO

RTS

In

how

man

y o

rders

can

th

e t

op

fiv

e f

inis

hers

in

a r

ace

fin

ish

? 120

22. JU

DIC

IAL P

RO

CED

UR

E T

he c

ou

rt s

yst

em

in

a c

om

mu

nit

y n

eed

s to

ass

ign

3 o

ut

of

8 j

ud

ges

to a

dock

et

of

crim

inal

case

s. F

ive o

f th

e j

ud

ges

are

male

an

d t

hre

e a

re f

em

ale

.

a.

Does

the s

ele

ctio

n o

f ju

dges

involv

e a

perm

uta

tion

or

a c

om

bin

ati

on

? co

mb

inati

on

b.

In h

ow

man

y w

ays

cou

ld t

hre

e j

ud

ges

be c

hose

n?

56

c.

If t

he j

ud

ges

are

ch

ose

n r

an

dom

ly,

wh

at

is t

he p

robabil

ity t

hat

all

3 j

ud

ges

are

male

? 5

28 , o

r ab

ou

t 18%

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-4

Ch

ap

ter

12

27

Gle

ncoe A

lgeb

ra 1

12-4

Wo

rd

Pro

ble

m P

racti

ce

Perm

uta

tio

ns a

nd

Co

mb

inati

on

s

1. C

HO

RES

In

Ash

ley’s

fam

ily t

here

are

4

chil

dre

n a

nd

th

eir

moth

er

an

d f

ath

er.

If

two o

f th

e s

ix m

ust

help

cle

ar

the t

able

aft

er

din

ner,

how

man

y w

ays

can

tw

o

peop

le b

e p

air

ed

? 15

2. PU

BLIC

SER

VIC

E A

cou

nty

com

pu

ter

ran

dom

ly s

ele

cts

juro

rs f

rom

th

e l

aw

yer-

ap

pro

ved

pote

nti

al

juro

r li

st.

How

man

y

ways

are

th

ere

for

12 j

uro

rs t

o b

e c

hose

n

from

a p

ool

of

20?

125,9

70

Po

ten

tial

Ju

rors

Fre

dJennifer

Sally

Carla

Mik

eS

am

Tom

Sylv

ia

Maria

Jam

al

Ted

Gre

g

Carlos

Todd

Doro

thy

Laure

n

Irene

Maya

Trish

Luke

3. SPO

RTS

H

an

s’ b

ask

etb

all

team

d

eci

des

to c

hoose

tw

o c

ap

tain

s each

w

eek

so t

hat

man

y p

layers

get

the

chan

ce t

o b

e c

ap

tain

. E

ach

week

, each

of

the 1

1 p

layers

wri

tes

his

nam

e o

n a

sl

ip o

f p

ap

er.

Th

e p

ap

ers

are

th

en

p

lace

d i

n a

con

tain

er

an

d m

ixed

. T

he

last

week

’s c

ap

tain

s d

raw

tw

o s

lip

s of

pap

er

from

th

e c

on

tain

er;

th

ese

tw

o

peop

le a

re c

ap

tain

s fo

r th

e f

oll

ow

ing

week

. H

ow

man

y d

iffe

ren

t p

air

s of

cap

tain

s ca

n b

e f

orm

ed

? 55

4.P

UZ

ZLE

S A

pop

ula

r n

ew

spap

er

pu

zzle

in

volv

es

a s

eri

es

of

lett

ers

th

at

can

be

rearr

an

ged

to f

orm

a w

ord

. W

ill

is

wri

tin

g h

is o

wn

vers

ion

of

the g

am

e f

or

a

sch

ool

pro

ject

. H

e w

an

ts t

o s

cram

ble

th

e

foll

ow

ing w

ord

for

his

pu

zzle

.

numbers

How

man

y w

ays

are

th

ere

to a

rran

ge

the l

ett

ers

wit

h t

he l

ett

er b

as

the f

irst

lett

er?

720

5. H

OR

SE R

AC

ING

In

th

e 1

33rd

ru

nn

ing

of

the K

en

tuck

y D

erb

y i

n 2

007,

there

w

ere

22 c

on

ten

ders

.

a.

How

man

y d

iffe

ren

t w

ays

can

th

e

hors

es

fin

ish

th

e r

ace

?

22!

b.

How

man

y d

iffe

ren

t w

ays

can

hors

es

pla

ce f

irst

, se

con

d,

an

d t

hir

d?

6840

c.

If a

ll 2

2 h

ors

es

have a

n e

qu

al

chan

ce

of

win

nin

g a

nd

3 o

f th

e h

ors

es

are

fe

male

, w

hat

is t

he p

robabil

ity t

hat

a

fem

ale

hors

e p

lace

s fi

rst,

seco

nd

, an

d

thir

d?

6

22!

Answers (Lesson 12-4)

Page 12: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A13 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

28

Gle

ncoe A

lgeb

ra 1

12-4

En

rich

men

t

A G

reat

Piz

za D

eal

A t

ele

vis

ion

com

merc

ial

ad

vert

ised

a p

izza d

eal

in w

hic

h c

ust

om

ers

cou

ld c

hoose

tw

o p

izzas

each

wit

h u

p t

o f

ive t

op

pin

gs

chose

n f

rom

a s

et

of

ele

ven

top

pin

gs.

On

th

e c

om

merc

ial,

a b

oy

claim

s th

at

there

are

1024

2 o

r 1,0

48,5

76 w

ays

for

the c

ust

om

er

to c

hoose

th

e t

wo p

izzas.

Is

this

a v

ali

d c

laim

?

Fo

r a lim

ited

tim

e, yo

u c

an

ch

oo

se 2

piz

zas w

ith

up

to

5 t

op

pin

gs f

or

on

ly

Piz

za D

eal!

!

$7.9

9!!

!!!!

!

To

pp

ing

Pep

pero

ni

Sau

sage

Tom

ato

Gre

en o

lives

Bla

ck o

lives

Mus

hroo

ms

Ext

ra C

hees

e

Pep

pers

Oni

ons

Pin

eapp

le

Ham

Yes

No

1. S

up

pose

th

e c

ust

om

er

can

have a

s m

an

y t

op

pin

gs,

up

to e

leven

, as

desi

red

. U

sin

g

cou

nti

ng t

ech

niq

ues,

how

man

y d

iffe

ren

t w

ays

can

th

e p

izzas

be m

ad

e?

(Hin

t: I

magin

e

that

the c

ust

om

er

has

to c

hoose

“yes”

or

“no”

for

each

top

pin

g.)

2

11 o

r 2048

2. U

se c

om

bin

ati

on

s to

dete

rmin

e h

ow

man

y w

ays

the c

ust

om

er

can

mak

e o

ne p

izza w

ith

up

to f

ive t

op

pin

gs.

C

(11,

0)

+ C

(11,

1)

+ C

(11,

2)

+ C

(11,

3)

+ C

(11,

4)

+

C(1

1,

5)

or

1024

3. H

ow

man

y w

ays

can

th

e t

wo p

izzas

be b

uil

t if

th

e t

hey a

re i

den

tica

l? 1024

4. H

ow

man

y w

ays

can

th

e t

wo p

izzas

be b

uil

t if

th

e t

hey a

re d

iffe

ren

t? (

Hin

t:

Use

th

e

tota

l n

um

ber

of

ways

that

on

e p

izza c

an

be m

ad

e f

rom

pro

ble

m 2

an

d t

hen

ch

oose

2 o

f

those

poss

ibil

itie

s.)

Sh

ou

ld y

ou

use

a c

om

bin

ati

on

or

a p

erm

uta

tion

? co

mb

inati

on

; C

(1024,

2)

or

523,7

76

5. A

dd

th

e r

esu

lts

from

pro

ble

ms

3 a

nd

4 t

o d

ete

rmin

e t

he t

ota

l n

um

ber

of

ways

to m

ak

e

two p

izzas

wit

h u

p t

o f

ive t

op

pin

gs

each

. 524,8

00

6. T

he b

oy i

n t

he a

d c

laim

s th

at

the c

ust

om

er

has

1024

2 c

hoic

es.

Wh

at

is 1

024

2?

How

does

this

com

pare

to t

he c

laim

mad

e b

y t

he b

oy i

n t

he a

dvert

isem

en

t? 1,0

48,5

76;

Yo

u

actu

ally h

ave a

lo

t fe

wer

ch

oic

es t

han

th

e b

oy c

laim

s.

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-5

Ch

ap

ter

12

29

Gle

ncoe A

lgeb

ra 1

12-5

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n

Pro

bab

ilit

y o

f C

om

po

un

d E

ven

ts

Ind

ep

en

den

t an

d D

ep

en

den

t Even

ts

Co

mp

ou

nd

ev

en

ts a

re m

ad

e u

p o

f tw

o o

r m

ore

sim

ple

even

ts.

Th

e e

ven

ts c

an

be i

nd

ep

en

den

t ev

en

ts o

r th

ey c

an

be d

ep

en

den

t ev

en

ts.

Pro

bab

ilit

y o

f In

dep

en

den

t E

ven

ts

Outc

om

e o

f firs

t event

does

not

affect

outc

om

e o

f second.

P(A

and B

) =

P(A

)

P(B

)

Exam

ple

: ro

lling a

6 o

n a

die

and

then r

olli

ng a

5

Pro

bab

ilit

y o

f D

ep

en

den

t E

ven

ts

Outc

om

e o

f firs

t event

does

affect

outc

om

e o

f second.

P(A

and B

) =

P(A

)

P(B

follo

win

g A

)

Exam

ple

: w

ithout

repla

cin

g t

he

firs

t card

, choosin

g a

n a

ce a

nd

then a

kin

g f

rom

a d

eck o

f card

s

F

ind

th

e p

ro

ba

bil

ity

tha

t y

ou

wil

l ro

ll a

six

an

d t

hen

a

fiv

e w

hen

yo

u r

oll

a d

ie t

wic

e.

By t

he d

efi

nit

ion

of

ind

ep

en

den

t even

ts, P

(A a

nd

B) =

P(A

) P

(B)

Fir

st r

oll

: P

(6) =

1

6

Seco

nd

roll

: P

(5) =

1

6

P(6

an

d 5

) =

P(6

) P

(5)

= 1

6

1

6

=

1

36

Th

e p

robabil

ity t

hat

you

wil

l ro

ll a

six

an

d t

hen

roll

a f

ive i

s 1

36 .

A

ba

g c

on

tain

s 3

red

ma

rb

les,

2 g

reen

ma

rb

les,

an

d 4

blu

e

ma

rb

les.

Tw

o m

arb

les a

re d

ra

wn

ra

nd

om

ly

fro

m t

he b

ag

an

d n

ot

rep

laced

. F

ind

th

e

pro

ba

bil

ity

th

at

bo

th m

arb

les a

re b

lue.

By t

he d

efi

nit

ion

of

dep

en

den

t even

ts,

P(A

an

d B

) =

P(A

) P

(B f

oll

ow

ing A

)

Fir

st m

arb

le: P

(blu

e) =

4

9

Seco

nd

marb

le: P

(blu

e) =

3

8

P(b

lue,

blu

e) =

4

9

3

8

= 1

2

72

= 1

6

Th

e p

robabil

ity o

f d

raw

ing t

wo b

lue m

arb

les

is 1

6 .

Exerc

ises

A b

ag

co

nta

ins 3

red

, 4 b

lue,

an

d 6

yell

ow

ma

rb

les.

On

e m

arb

le i

s s

ele

cte

d a

t a

tim

e,

an

d o

nce a

ma

rb

le i

s s

ele

cte

d,

it i

s n

ot

rep

laced

. F

ind

ea

ch

pro

ba

bil

ity

.

1.

P(2

yell

ow

) 5

26

2. P

(red

, yell

ow

) 3

26

3. P

(blu

e,

red

, yell

ow

)

6

143

4. G

eorg

e h

as

two r

ed

sock

s an

d t

wo w

hit

e s

ock

s in

a d

raw

er.

Wh

at

is t

he p

robabil

ity o

f p

ick

ing a

red

sock

an

d a

wh

ite s

ock

in

th

at

ord

er

if t

he f

irst

sock

is

not

rep

lace

d?

5. P

hyll

is d

rop

s a p

en

ny i

n a

pon

d,

an

d t

hen

sh

e d

rop

s a n

ick

el

in t

he p

on

d.

Wh

at

is t

he

pro

babil

ity t

hat

both

coin

s la

nd

wit

h t

ail

s sh

ow

ing?

6. A

die

is

roll

ed

an

d a

pen

ny i

s d

rop

ped

. F

ind

th

e p

robabil

ity o

f ro

llin

g a

tw

o a

nd

sh

ow

ing

a t

ail

.

Exam

ple

1Exam

ple

2

1

4

1

3

1

12

Answers (Lesson 12-4 and Lesson 12-5)

Page 13: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A14 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

30

Gle

ncoe A

lgeb

ra 1

12-5

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n (c

on

tin

ued

)

Pro

bab

ilit

y o

f C

om

po

un

d E

ven

ts

Mu

tually E

xcl

usi

ve a

nd

In

clu

sive E

ven

ts

Even

ts t

hat

can

not

occ

ur

at

the s

am

e

tim

e a

re c

all

ed

mu

tuall

y e

xcl

usi

ve.

If t

wo e

ven

ts a

re n

ot

mu

tuall

y e

xcl

usi

ve,

they a

re c

all

ed

in

clu

sive.

Pro

bab

ilit

y o

f M

utu

ally

Exclu

siv

e E

ven

tsP

(A o

r B

) =

P(A

) +

P(B

)P

(rolli

ng a

2 o

r a 3

on a

die

) =

P(2

) +

P(3

) =

1 −

3

Pro

bab

ilit

y o

f

Inclu

siv

e E

ven

ts

P(A

or

B) =

P(A

) +

P(B

) -

P(A

and B

)P

(kin

g o

r heart

) =

P(K

) +

P(H

) -

P(K

and H

) =

9 −

26

A

ca

rd

is d

ra

wn

fro

m a

sta

nd

ard

deck

of

pla

yin

g c

ard

s.

Fin

d t

he

pro

ba

bil

ity

of

dra

win

g a

kin

g o

r a

qu

een

.

Dra

win

g a

kin

g o

r a q

ueen

are

mu

tuall

y e

xcl

usi

ve e

ven

ts.

By t

he d

efi

nit

ion

of

mu

tuall

y e

xcl

usi

ve e

ven

ts,

P(A

or

B) =

P(A

) +

P(B

).

P(A

) =

P(k

ing) =

4 −

52 =

1 −

13

P(B

) =

P(q

ueen

) =

4 −

52 =

1 −

13

P(k

ing o

r qu

een

) =

1 −

13 +

1 −

13

=

2 −

13

Th

e p

robabil

ity o

f d

raw

ing a

kin

g o

r a q

ueen

is

2 −

13 .

Exerc

ises

A b

ag

co

nta

ins 2

red

, 5 b

lue,

an

d 7

yell

ow

ma

rb

les.

Fin

d e

ach

pro

ba

bil

ity

.

1.

P(y

ell

ow

or

red

) 9

14

2.

P(r

ed

or

not

yell

ow

) 1

2

3. P

(blu

e o

r re

d o

r yell

ow

) 1

A c

ard

is d

ra

wn

fro

m a

sta

nd

ard

deck

of

pla

yin

g c

ard

s.

Fin

d e

ach

pro

ba

bil

ity

.

4.

P(j

ack

or

red

) 7

13

5. P

(red

or

bla

ck)

1

6.

P(j

ack

or

clu

bs)

4

13

7. P

(qu

een

or

less

th

an

3)

3

13

8.

P(5

or

6)

2

13

9. P

(dia

mon

d o

r sp

ad

e)

1

2

10. In

a m

ath

cla

ss,

12 o

ut

of

15 g

irls

are

14 y

ears

old

an

d 1

4 o

ut

of

17 b

oys

are

14 y

ears

old

. W

hat

is t

he p

robabil

ity o

f se

lect

ing a

gir

l or

a 1

4-y

ear

old

fro

m t

his

cla

ss?

Exam

ple

29

32

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-5

Ch

ap

ter

12

31

Gle

ncoe A

lgeb

ra 1

12-5

Sk

ills

Pra

ctic

e

Pro

bab

ilit

y o

f C

om

po

un

d E

ven

tsA

ba

g c

on

tain

s 2

green

, 9 b

ro

wn

, 7 y

ell

ow

, a

nd

4 b

lue m

arb

les.

On

ce a

ma

rb

le i

s

sele

cte

d,

it i

s n

ot

rep

laced

. F

ind

ea

ch

pro

ba

bil

ity

.

1. P

(bro

wn

, th

en

yell

ow

) 3

22

2. P

(gre

en

, th

en

blu

e)

4

231

3. P

(yell

ow

, th

en

yell

ow

) 1

11

4. P

(blu

e,

then

blu

e)

2

77

5. P

(gre

en

, th

en

not

blu

e)

17

231

6. P

(bro

wn

, th

en

not

gre

en

) 5

7

154

A d

ie i

s r

oll

ed

an

d a

sp

inn

er l

ike t

he o

ne a

t

the r

igh

t is

sp

un

. F

ind

ea

ch

pro

ba

bil

ity

.

7.

P(4

an

d A

) 1

24

8.

P(a

n e

ven

nu

mber

an

d C

) 1

8

9.

P(2

or

5 a

nd

B o

r D

) 1

6

10.

P(a

nu

mber

less

th

an

5 a

nd

B,

C,

or

D)

1

2

A c

ard

is b

ein

g d

ra

wn

fro

m a

sta

nd

ard

deck

of

pla

yin

g c

ard

s. D

ete

rm

ine w

heth

er t

he

ev

en

ts a

re m

utu

all

y e

xclu

sive o

r n

ot

mu

tua

lly

ex

clu

siv

e. T

hen

fin

d t

he p

ro

ba

bil

ity

.

11. P

(jack

or

ten

) m

utu

ally e

xclu

siv

e;

2

13

12.

P(r

ed o

r bla

ck)

mu

tually e

xclu

siv

e; 1

13. P

(qu

een

or

clu

b)

no

t;

4

13

14.

P(r

ed

or

ace

) n

ot;

7

13

15. P

(dia

mon

d o

r bla

ck)

mu

tually e

xclu

siv

e;

3

4

16.

P(f

ace

card

or

spad

e)

n

ot;

1

1

26

Til

es n

um

bered

1 t

hro

ug

h 2

0 a

re p

laced

in

a b

ox

. T

iles n

um

bered

11 t

hro

ug

h 3

0

are p

laced

in

a s

eco

nd

bo

x.

Th

e f

irst

tile

is r

an

do

mly

dra

wn

fro

m t

he f

irst

bo

x.

Th

e s

eco

nd

til

e i

s r

an

do

mly

dra

wn

fro

m t

he s

eco

nd

bo

x.

Fin

d e

ach

pro

ba

bil

ity

.

17. P

(both

are

gre

ate

r th

an

15)

3

16

18. T

he f

irst

til

e i

s od

d a

nd

th

e s

eco

nd

til

e i

s le

ss t

han

25.

7

20

19. T

he f

irst

til

e i

s a m

ult

iple

of

6 a

nd

th

e s

eco

nd

til

e i

s a m

ult

iple

of

4.

3

80

20. T

he f

irst

til

e i

s le

ss t

han

15 a

nd

th

e s

eco

nd

til

e i

s even

or

gre

ate

r th

an

25.

21

50

A C

BD

Answers (Lesson 12-5)

Page 14: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A15 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

32

Gle

ncoe A

lgeb

ra 1

Practi

ce

Pro

bab

ilit

y o

f C

om

po

un

d E

ven

tsA

ba

g c

on

tain

s 5

red

, 3 b

ro

wn

, 6 y

ell

ow

, a

nd

2 b

lue m

arb

les.

On

ce a

ma

rb

le i

s

sele

cte

d,

it i

s n

ot

rep

laced

. F

ind

ea

ch

pro

ba

bil

ity

.

1. P

(bro

wn

, th

en

yell

ow

, th

en

red

)

3

112

2. P

(red

, th

en

red

, th

en

blu

e)

1

84

3. P

(yell

ow

, th

en

yell

ow

, th

en

not

blu

e)

3

28

4. P

(bro

wn

, th

en

bro

wn

, th

en

not

yell

ow

) 1

70

A d

ie i

s r

oll

ed

an

d a

ca

rd

is d

ra

wn

fro

m a

sta

nd

ard

deck

of

52 c

ard

s.

Fin

d e

ach

pro

ba

bil

ity

.

5. P

(6 a

nd

kin

g)

1

78

6. P

(od

d n

um

ber

an

d b

lack

) 1

4

7. P

(less

th

an

3 a

nd

heart

) 1

12

8. P

(gre

ate

r th

an

1 a

nd

bla

ck a

ce)

5

156

A c

ard

is b

ein

g d

ra

wn

fro

m a

sta

nd

ard

deck

of

pla

yin

g c

ard

s.

Dete

rm

ine w

heth

er

the e

ven

ts a

re m

utu

all

y e

xclu

siv

e o

r n

ot

mu

tua

lly

ex

clu

siv

e.

Th

en

fin

d t

he

pro

ba

bil

ity

.

9. P

(sp

ad

e o

r n

um

bere

d c

ard

) 4

3

52

10. P

(ace

or

red

qu

een

) 3

26

11. P

(red

or not

face

card

) 2

3

26

12. P

(heart

or not

qu

een

) 4

9

52

Til

es n

um

bered

1 t

hro

ug

h 2

5 a

re p

laced

in

a b

ox

. T

iles n

um

bered

11 t

hro

ug

h 3

0

are p

laced

in

a s

eco

nd

bo

x.

Th

e f

irst

tile

is r

an

do

mly

dra

wn

fro

m t

he f

irst

bo

x.

Th

e s

eco

nd

til

e i

s r

an

do

mly

dra

wn

fro

m t

he s

eco

nd

bo

x.

Fin

d e

ach

pro

ba

bil

ity

.

13. P

(both

are

gre

ate

r th

an

15 a

nd

less

th

an

20)

4

125

14. T

he f

irst

til

e i

s gre

ate

r th

an

10 a

nd

th

e s

eco

nd

til

e i

s le

ss t

han

25 o

r even

. 5

1

100

15. T

he f

irst

til

e i

s a m

ult

iple

of

3 o

r p

rim

e a

nd

th

e s

eco

nd

til

e i

s a m

ult

iple

of

5.

16

125

16. T

he f

irst

til

e i

s le

ss t

han

9 o

r od

d a

nd

th

e s

eco

nd

til

e i

s a m

ult

iple

of

4 o

r le

ss t

han

21.

51

125

17. W

EA

TH

ER

T

he f

ore

cast

pre

dic

ts a

40%

ch

an

ce o

f ra

in o

n T

uesd

ay a

nd

a 6

0%

ch

an

ce o

n

Wed

nesd

ay.

If t

hese

pro

babil

itie

s are

in

dep

en

den

t, w

hat

is t

he c

han

ce t

hat

it w

ill

rain

on

both

days?

24%

18. FO

OD

T

om

aso

pla

ces

favori

te r

eci

pes

in a

bag f

or

4 p

ast

a d

ish

es,

5 c

ass

ero

les,

3 t

yp

es

of

chil

i, a

nd

8 d

ess

ert

s.

a.

If T

om

aso

ch

oose

s on

e r

eci

pe a

t ra

nd

om

, w

hat

is t

he p

robabil

ity t

hat

he s

ele

cts

a

past

a d

ish

or

a c

ass

ero

le?

9

20

b.

If T

om

aso

ch

oose

s on

e r

eci

pe a

t ra

nd

om

, w

hat

is t

he p

robabil

ity t

hat

he d

oes not

sele

ct a

dess

ert

? 3

5

c.

If T

om

aso

ch

oose

s tw

o r

eci

pes

at

ran

dom

wit

hou

t re

pla

cem

en

t, w

hat

is t

he p

robabil

ity

that

the f

irst

reci

pe h

e s

ele

cts

is a

cass

ero

le a

nd

th

e s

eco

nd

reci

pe h

e s

ele

cts

is a

d

ess

ert

? 2

19

12-5

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-5

Ch

ap

ter

12

33

Gle

ncoe A

lgeb

ra 1

Wo

rd

Pro

ble

m P

racti

ce

Pro

bab

ilit

y o

f C

om

po

un

d E

ven

ts

1.B

IRTH

DA

YS

O

n J

uan

ita’s

bir

thd

ay,

her

gra

nd

moth

er

sen

ds

her

a c

ard

. W

hat

is

the p

robabil

ity t

hat

the m

an

wh

o

deli

vere

d t

he m

ail

has

a b

irth

day e

ith

er

the s

am

e d

ay o

r on

e d

ay b

efo

re o

r aft

er?

D

isre

gard

Febru

ary

29 a

s a p

oss

ible

bir

thd

ay,

an

d a

ssu

me t

hat

all

days

are

equ

all

y l

ikely

.

≈ 0

.82%

2. SPO

RTS

T

he W

orl

d S

eri

es

is a

“best

of

seven

” gam

e c

ham

pio

nsh

ip i

n w

hic

h u

p

to s

even

gam

es

are

pla

yed

, an

d o

ne t

eam

h

as

to w

in f

ou

r gam

es

to w

in t

he S

eri

es.

In

th

e 2

007 W

orl

d S

eri

es,

th

e B

ost

on

Red

S

ox s

wep

t th

e C

olo

rad

o R

ock

ies,

mean

ing

that

they w

on

th

e s

eri

es

by w

inn

ing t

he

firs

t fo

ur

gam

es.

If

you

ass

um

e t

hat

each

te

am

has

an

equ

al

chan

ce o

f w

inn

ing

each

gam

e,

wh

at

is t

he p

robabil

ity o

f a

Worl

d S

eri

es

sweep

?

0.0

625 o

r 6.2

5%

3. B

USIN

ESS

A

t C

orr

ugate

d P

ack

agin

g,

Inc.

, a t

eam

of

six e

mp

loyees

is i

n c

harg

e

of

mark

eti

ng a

nd

sell

ing t

he c

om

pan

y’s

p

rod

uct

s; t

hre

e a

re w

om

en

an

d t

hre

e a

re

men

. T

he p

resi

den

t of

the c

om

pan

y

deci

des

to s

en

d f

ou

r te

am

mem

bers

to a

n

ati

on

al

card

board

box c

on

fere

nce

. H

e

wan

ts t

o m

ak

e s

ure

he c

hoose

s n

am

es

fair

ly,

so h

e d

eci

des

to p

ut

the n

am

es

of

his

six

sale

s em

plo

yees

in a

hat

an

d d

raw

fo

ur

nam

es

to s

ee w

ho w

ill

go t

o t

he

con

fere

nce

. W

hat

is t

he p

robabil

ity t

hat

the t

eam

wil

l co

nsi

st o

f th

ree w

om

en

an

d

on

e m

an

? 0.2

or

20%

4.M

AG

IC Ir

is p

erf

orm

s a m

agic

tri

ck i

n

wh

ich

sh

e h

old

s a s

tan

dard

deck

of

card

s an

d h

as

each

of

thre

e p

eop

le r

an

dom

ly

choose

a c

ard

fro

m t

he d

eck

. E

ach

pers

on

k

eep

s h

is o

r h

er

card

as

the n

ext

pers

on

d

raw

s. W

hat

is t

he p

robabil

ity t

hat

all

th

ree p

eop

le w

ill

dra

w a

heart

?

0

.0129 o

r 1.2

9%

10

10

5

5

7

7

Q

Q

4

4

K

K

6

6

2

2

J

J

9

9

3

3

A

A

8

8

5. STO

CK

S B

ruce

has

just

pu

rch

ase

d 1

00

share

s of

Ou

t C

lon

e,

Inc.

sto

ck.

Th

e

com

pan

y i

s se

ek

ing F

DA

ap

pro

val

for

a

treatm

en

t th

at

reli

eves

the c

om

mon

cold

. A

ccord

ing t

o p

harm

ace

uti

cal

exp

ert

s,

there

is

a 5

0%

ch

an

ce t

hat

FD

A a

pp

roval

wil

l be g

ran

ted

, an

d a

ccord

ing t

o m

ark

et

insi

ders

th

ere

is

an

85%

ch

an

ce t

he v

alu

e

of

the s

tock

wil

l d

ou

ble

if

FD

A a

pp

roval

is g

ran

ted

.

a.

Wh

at

is t

he p

robabil

ity t

hat

the F

DA

w

ill

ap

pro

ve t

he t

reatm

en

t an

d t

he

valu

e o

f B

ruce

’s i

nvest

men

t w

ill

dou

ble

? 0.4

25 o

r 42.5

%

b.

Wh

at

is t

he p

robabil

ity t

hat

the F

DA

w

ill

ap

pro

ve t

he t

reatm

en

t an

d t

he

valu

e o

f you

r st

ock

wil

l n

ot

dou

ble

?

0.0

75 o

r 7.5

%

c.

Are

th

ese

even

ts d

ep

en

den

t or

ind

ep

en

den

t? D

ep

en

den

t; t

he

pro

bab

ilit

y t

hat

the s

tock p

rice

will

do

ub

le d

ep

en

ds o

n t

he

pro

bab

ilit

y t

hat

the t

reatm

en

t w

ill

be a

pp

roved

.

12-5

Answers (Lesson 12-5)

Page 15: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A16 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

34

Gle

ncoe A

lgeb

ra 1

12-5

Hap

py B

irth

day

On

a r

eali

ty s

how

, a c

on

test

an

t m

ust

ran

dom

ly c

hoose

en

ou

gh

peop

le t

o g

o i

nto

a r

oom

so

that

the p

robabil

ity t

hat

at

least

on

e o

f th

ose

peop

le h

as

the s

am

e b

irth

day (

mon

th a

nd

d

ate

) as

the c

on

test

an

t is

gre

ate

r th

an

50%

. T

ime i

s of

the e

ssen

ce,

so t

he c

on

test

an

t d

oesn

’t

wan

t an

y m

ore

peop

le t

han

nece

ssary

. W

hat

nu

mber

of

peop

le s

hou

ld t

he c

on

test

an

t gath

er?

1. M

ak

e a

con

ject

ure

abou

t th

e n

um

ber

of

peop

le n

eed

ed

. A

nsw

ers

will

vary

. A

co

mm

on

gu

ess i

s a

bo

ut

187.

2. W

hen

th

e p

robabil

ity t

hat

every

pers

on

in

th

e r

oom

has

a d

iffe

ren

t bir

thd

ay i

s le

ss t

han

50%

, th

e p

robabil

ity t

hat

two o

f th

em

wil

l sh

are

a b

irth

day i

s gre

ate

r th

an

50%

. E

xp

lain

wh

y.

S

am

ple

An

sw

er:

Becau

se i

f th

e p

rob

ab

ilit

y i

s l

ess t

han

50%

, th

en

th

e c

om

ple

men

t w

ill

be 1

– w

hic

h w

ill

be g

reate

r th

an

50%

.

3. O

bse

rve t

his

patt

ern

:

If

th

ere

are

tw

o p

eop

le i

n t

he r

oom

, th

e p

robabil

ity t

hat

they a

ll h

ave d

iffe

ren

t

bir

thd

ays

is 3

65

365 ·

364

365 o

r 99.7

%.

If

th

ere

are

th

ree p

eop

le i

n t

he r

oom

, th

e p

robabil

ity t

hat

they a

ll h

ave d

iffe

ren

t

bir

thd

ays

is 3

65

365 ·

364

365 ·

363

365 o

r 99.2

%.

If

th

ere

are

fou

r p

eop

le i

n t

he r

oom

, th

e p

robabil

ity t

hat

they a

ll h

ave d

iffe

ren

t

bir

thd

ays

is 3

65

365 ·

364

365 ·

363

365 ·

362

365 o

r 99.2

%.

E

xte

nd

th

is p

att

ern

un

til

you

get

a p

robabil

ity l

ess

th

an

50%

. H

ow

man

y p

eop

le d

o y

ou

need

to g

et

a p

robabil

ity l

ess

th

an

50%

? 24 p

eo

ple

4. S

o,

how

man

y p

eop

le d

o y

ou

need

to h

ave i

n a

room

so t

hat

the p

robabil

ity o

f tw

o o

f th

em

sh

ari

ng a

bir

thd

ay i

s gre

ate

r th

an

50%

? H

ow

does

this

com

pare

to y

ou

r an

swer

to

pro

ble

m 1

? 24 p

eo

ple

; see s

tud

en

ts’

wo

rk.

5. U

se t

he m

eth

od

above t

o d

ete

rmin

e h

ow

man

y p

eop

le w

ou

ld n

eed

to b

e i

n a

room

so t

hat

the p

robabil

ity o

f tw

o o

f th

em

havin

g b

irth

days

on

th

e s

am

e d

ay o

f th

e m

on

th i

s gre

ate

r th

an

50%

. 7 p

eo

ple

En

rich

men

t

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-5

Ch

ap

ter

12

35

Gle

ncoe A

lgeb

ra 1

12-5

TI-

Nsp

ire A

ctiv

ity

Pro

bab

ilit

y o

f C

om

po

un

d E

ven

tsT

he T

I-N

spir

e c

alc

ula

tor

can

be u

sed

to e

valu

ate

perm

uta

tion

s an

d

com

bin

ati

on

s u

sin

g t

he f

un

ctio

ns

nP

r a

nd

nC

r,

resp

ect

ively

.

a. P

(8,

3)

Calc

ula

te t

he n

um

ber

of

perm

uta

tion

s of

eig

ht

obje

cts

tak

en

th

ree a

t a t

ime.

Keyst

rok

es:

N P R ( 8 , 3 ) ·

.

b. C

(8,

3)

Calc

ula

te t

he n

um

ber

of

com

bin

ati

on

s of

eig

ht

obje

cts

tak

en

th

ree a

t a t

ime.

Keyst

rok

es:

N C R ( 8 , 3 ) ·

.

W

ha

t is

th

e p

ro

ba

bil

ity

of

dra

win

g f

ive c

ard

s f

ro

m a

sta

nd

ard

deck

of

ca

rd

s a

nd

ha

vin

g t

hree o

f th

e c

ard

s b

e a

ces?

Wri

te t

he p

robabil

ity a

s th

e p

rod

uct

of

com

bin

ati

on

s fo

r h

avin

g t

hre

e a

ces

over

the t

ota

l co

mbin

ati

on

s fo

ran

y f

ive c

ard

s,

. C

alc

ula

te t

he p

robabil

ity

usi

ng t

he n

Cr c

om

man

d.

Keyst

rok

es:

N C R ( 1

3 , 1 ) r N C R

( 4 , 3 ) r N C R ( 4

8 , 2 ) pN C R

( 5

2 , 5 ) ·

.

Th

e p

robabil

ity i

s

94

4165 .

Exerc

ises

Ev

alu

ate

ea

ch

ex

pressio

n.

1. P

(8,

5)

6720

2. C

(12,

8)

49

5

3. P

(7,

3)

21

0

4. C

(52,

5)

2,5

98,9

60

5. P

(9,

4)

3024

6. C

(48,

4)

194,5

80

7. P

(13,

4)

17,1

60

8. C

(36,

5)

376,9

92

Fin

d e

ach

pro

ba

bil

ity

.

9. W

hat

is t

he p

robabil

ity o

f d

raw

ing f

ou

r 2s

wh

en

sele

ctin

g f

ive c

ard

s fr

om

a s

tan

dard

deck

of

card

s?

48

C(5

2, 5) =

48

2,5

98,9

60

=

1

54,1

45

10. W

hat

is t

he p

robabil

ity o

f ro

llin

g f

ive d

ice a

nd

all

of

them

sh

ow

ing t

he s

am

e n

um

ber?

1

1296

Exam

ple

1

Exam

ple

2

C(1

3, 1)

· C

(4,

3)

· C

(48,

2)

−−

C(5

2,

5)

Ev

alu

ate

ea

ch

ex

pressio

n.

Answers (Lesson 12-5)

Page 16: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A17 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

36

Gle

ncoe A

lgeb

ra 1

12-6

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n

Pro

bab

ilit

y D

istr

ibu

tio

ns

Ran

do

m V

ari

ab

les

an

d P

rob

ab

ilit

y

A r

an

do

m v

aria

ble

X i

s a v

ari

able

wh

ose

valu

e i

s th

e n

um

eri

cal

ou

tcom

e o

f a r

an

dom

even

t.

A

tea

ch

er a

sk

ed

her s

tud

en

ts h

ow

ma

ny

sib

lin

gs t

hey

ha

ve.

Th

e r

esu

lts a

re s

ho

wn

in

th

e t

ab

le a

t

the r

igh

t.

a.

Fin

d t

he p

ro

ba

bil

ity

th

at

a r

an

do

mly

sele

cte

d s

tud

en

t

ha

s 2

sib

lin

gs.

T

he r

an

dom

vari

able

X c

an

equ

al

0,

1,

2,

3,

or

4.

In t

he t

able

, th

e v

alu

e X

= 2

is

pair

ed

wit

h 8

ou

tcom

es,

an

d t

here

are

27 s

tud

en

ts s

urv

eyed

.

P(X

= 2

) =

2 s

ibli

ngs

27 s

tud

en

ts s

urv

eyed

=

8

27

T

he p

robabil

ity t

hat

a r

an

dom

ly s

ele

cted

stu

den

t h

as

2 s

ibli

ngs

is

8

27 ,

or

29.6

%.

b.

Fin

d t

he p

ro

ba

bil

ity

th

at

a r

an

do

mly

sele

cte

d s

tud

en

t h

as a

t le

ast

three

sib

lin

gs.

P

(X ≥

3)

= 2

+ 1

27

T

he p

robabil

ity t

hat

a r

an

dom

ly s

ele

cted

stu

den

t h

as

at

least

3 s

ibli

ngs

is 1

9 ,

or

11.1

%.

Exerc

ises

Fo

r E

xercis

es 1

–3,

use t

he g

ra

de d

istr

ibu

tio

n

sh

ow

n a

t th

e r

igh

t. A

gra

de o

f A

= 5

, B

= 4

,

C =

3,

D =

2,

F =

1.

1. F

ind

th

e p

robabil

ity t

hat

a r

an

dom

ly s

ele

cted

st

ud

en

t in

th

is c

lass

rece

ived

a g

rad

e o

f C

. 1

5

2. F

ind

th

e p

robabil

ity t

hat

a r

an

dom

ly s

ele

cted

stu

den

t in

th

is c

lass

rece

ived

a g

rad

e

low

er

than

a C

. 1

5

3. W

hat

is t

he p

robabil

ity t

hat

a r

an

dom

ly s

ele

cted

stu

den

t in

th

is c

lass

pass

es

the c

ou

rse,

that

is,

gets

at

least

a D

? 2

4 −

25

4. T

he t

able

sh

ow

s th

e r

esu

lts

of

toss

ing 3

coin

s 50 t

imes.

Wh

at

is t

he p

robabil

ity o

f gett

ing

2 o

r 3 h

ead

s? 48%

Exam

ple

Nu

mb

er

of

Sib

lin

gs

Nu

mb

er

of

Stu

den

ts

01

115

28

32

41

X =

Gra

de

54

32

1

Nu

mb

er

of

stu

dets

69

54

1

X =

Nu

mb

er

of

Head

s0

12

3

Nu

mb

er

of

Tim

es

620

19

5

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Lesson 12-6

Ch

ap

ter

12

37

Gle

ncoe A

lgeb

ra 1

12-6

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n (c

on

tin

ued

)

Pro

bab

ilit

y D

istr

ibu

tio

ns

Pro

bab

ilit

y D

istr

ibu

tio

ns

Th

e p

robabil

itie

s ass

oci

ate

d w

ith

every

poss

ible

valu

e o

f th

e r

an

dom

vari

able

X m

ak

e u

p w

hat

are

call

ed

th

e p

ro

ba

bil

ity

dis

trib

uti

on

for

that

vari

able

. A

pro

babil

ity d

istr

ibu

tion

has

the f

oll

ow

ing p

rop

ert

ies.

Pro

pert

ies o

f a P

rob

ab

ilit

y

Dis

trib

uti

on

1.

The p

robabili

ty o

f each v

alu

e o

f X

is g

reate

r th

an o

r equal to

0.

2.

The p

robabili

ties f

or

all

valu

es o

f X

add u

p t

o 1

.

Th

e p

robabil

ity d

istr

ibu

tion

for

a r

an

dom

vari

able

can

be g

iven

in

a t

able

or

in a

p

ro

ba

bil

ity

his

tog

ra

m a

nd

use

d t

o o

bta

in o

ther

info

rmati

on

.

T

he d

ata

fro

m t

he e

xa

mp

le o

n t

he p

rev

iou

s p

ag

e c

an

be u

sed

to

dete

rm

ine a

pro

ba

bil

ity

dis

trib

uti

on

an

d t

o m

ak

e a

pro

ba

bil

ity

his

tog

ra

m.

X =

Nu

mb

er

of

Sib

lin

gs

P(X

)

00.0

37

10.5

56

20.2

96

30.0

74

40.0

37

0.600

0.400

0.200

0

P(X

)

X =

Nu

mb

er

of

Sib

lin

gs

Pro

bab

ilit

y H

isto

gra

m

12

34

a.

Sh

ow

th

at

the d

istr

ibu

tio

n

is v

ali

d.

For

each

valu

e o

f X

, th

e p

robabil

ity

is g

reate

r th

an

or

equ

al

to 0

an

d

less

th

an

or

equ

al

to 1

. A

lso,

the

sum

of

the p

robabil

itie

s is

1.

b.

Wh

at

is t

he p

ro

ba

bil

ity

th

at

a s

tud

en

t

ch

osen

at

ra

nd

om

ha

s f

ew

er t

ha

n

2 s

ibli

ng

s?

Beca

use

th

e e

ven

ts a

re i

nd

ep

en

den

t, t

he

pro

babil

ity o

f fe

wer

than

2 s

ibli

ngs

is t

he s

um

of

the p

robabil

ity o

f 0 s

ibli

ngs

an

d t

he

pro

babil

ity o

f 1 s

ibli

ng,

or

0.0

37 +

0.5

56 =

0.5

93.

Exerc

ises

Th

e t

ab

le a

t th

e r

igh

t sh

ow

s t

he p

ro

ba

bil

ity

dis

trib

uti

on

fo

r s

tud

en

ts b

y s

ch

oo

l en

ro

llm

en

t

in t

he U

nit

ed

Sta

tes i

n 2

000.

Use t

he t

ab

le f

or

Ex

ercis

es 1

– 3

.

1. S

how

th

at

the d

istr

ibu

tion

is

vali

d.

0

≤ P

(X) ≤

1;

the s

um

of

the p

rob

ab

ilit

ies =

1

2.

If a

stu

den

t is

ch

ose

n a

t ra

nd

om

, w

hat

is t

he p

robabil

ity

that

the s

tud

en

t is

in

ele

men

tary

or

seco

nd

ary

sch

ool?

0.7

77

3. M

ak

e a

pro

babil

ity h

isto

gra

m o

f th

e d

ata

.

1.0

0.8

0.6

0.4

0.2

1

P(X

)

X =

Typ

e o

f Sch

oo

l

Pro

bab

ilit

y H

isto

gra

m

23

So

urc

e:

U.S

. C

ensus B

ure

au

Exam

ple

X =

Typ

e o

f S

ch

oo

lP

(X)

Ele

menta

ry =

10.5

62

Secondary

= 2

0.2

15

Hig

her

Education =

30.2

23

Answers (Lesson 12-6)

Page 17: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A18 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

38

Gle

ncoe A

lgeb

ra 1

12-6

Sk

ills

Practi

ce

Pro

bab

ilit

y D

istr

ibu

tio

ns

Fo

r E

xercis

es 1

–3,

the s

pin

ner s

ho

wn

is s

pu

n t

hree t

imes.

1. W

rite

th

e s

am

ple

sp

ace

wit

h a

ll p

oss

ible

ou

tcom

es.

G

GG

, G

GB

, G

BG

, G

BB

, B

GG

, B

GB

, B

BG

, B

BB

2. F

ind

th

e p

robabil

ity d

istr

ibu

tion

X,

wh

ere

X r

ep

rese

nts

th

e n

um

ber

of

tim

es

the s

pin

ner

lan

ds

on

gre

en

for X

= 0

, X

= 1

, X

= 2

, an

d X

= 3

.

P(X

= 0

) =

0.1

25,

P(X

= 1

) =

0.3

75,

P(X

= 2

) =

0.3

75,

P(X

= 3

) =

0.1

25

3. M

ak

e a

pro

babil

ity h

isto

gra

m o

f th

e d

ata

.

Fo

r E

xercis

es 4

–6,

the s

pin

ner s

ho

wn

is s

pu

n t

wo

tim

es.

4. W

rite

th

e s

am

ple

sp

ace

wit

h a

ll p

oss

ible

ou

tcom

es.

R

R,

RB

, R

G,

R

Y,

BR

, B

B,

BG

, B

Y,

GR

, G

B,

GG

, G

Y,

YR

, Y

B,

YG

, Y

Y

5. F

ind

th

e p

robabil

ity d

istr

ibu

tion

X,

wh

ere

X r

ep

rese

nts

th

e n

um

ber

of

tim

es

the s

pin

ner

lan

ds

on

yell

ow

for X

= 0

, X

= 1

, an

d X

= 2

.

P(X

= 0

) =

0.5

625,

P(X

= 1

) =

0.3

75,

P(X

= 2

) =

0.0

625

6. M

ak

e a

pro

babil

ity h

isto

gra

m o

f th

e d

ata

.

7. B

USIN

ESS

U

se t

he t

able

th

at

show

s th

e

pro

babil

ity d

istr

ibu

tion

of

the n

um

ber

of

min

ute

s a c

ust

om

er

spen

ds

at

the e

xp

ress

ch

eck

ou

t at

a s

up

erm

ark

et.

a.

Sh

ow

th

at

the d

istr

ibu

tion

is

vali

d.

0.0

9 +

0.1

3 +

0.2

8 +

0.3

2 +

0.1

8 =

1

b.

Wh

at

is t

he p

robabil

ity t

hat

a c

ust

om

er

spen

ds

less

th

an

3 m

inu

tes

at

the c

heck

ou

t?

0.2

2

c.

Wh

at

is t

he p

robabil

ity t

hat

the c

ust

om

er

spen

ds

at

least

4 m

inu

tes

at

the c

heck

ou

t?

0.5

0

RED

BLUE

GREEN

YELLOW

BLUE

GREEN

X =

Min

ute

s1

23

45 +

Pro

bab

ilit

y0.0

90.1

30.2

80.3

20.1

8

0.4

0.3

0.2

0.1 0

0

P(X

)

X =

Nu

mb

er

of

Tim

es

Sp

inn

er

Lan

ds

on

Gre

en

Sp

inn

er

Pro

bab

ilit

yD

istr

ibu

tio

n

12

3

0.6

0.5

0.4

0.3

0.2

0.1 0

0

P(X

)

X =

Nu

mb

er

of

Tim

es

Sp

inn

er

Lan

ds

on

Yello

w

Sp

inn

er

Pro

bab

ilit

yD

istr

ibu

tio

n

12

Lesson 12-6

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

39

Gle

ncoe A

lgeb

ra 1

12-6

Practi

ce

Pro

bab

ilit

y D

istr

ibu

tio

ns

Fo

r E

xercis

es 1

–3,

the s

pin

ner s

ho

wn

is s

pu

n t

wo

tim

es.

1. W

rite

th

e s

am

ple

sp

ace

wit

h a

ll p

oss

ible

ou

tcom

es.

B

B,

BW

, B

R,

BY

, B

G,

WB

, W

W,

WR

, W

Y,

WG

, R

B,

RW

, R

R,

RY

, R

G,

YB

, Y

W,

YR

, Y

Y,

YG

, G

B,

GW

, G

R,

GY

, G

G

2. F

ind

th

e p

robabil

ity d

istr

ibu

tion

X,

wh

ere

X r

ep

rese

nts

th

e n

um

ber

of

tim

es

the s

pin

ner

lan

ds

on

blu

e f

or X

= 0

, X

= 1

, an

d X

= 2

.

P

(X =

0) =

0.6

4,

P(X

= 1

) =

0.3

2,

P(X

= 2

) =

0.0

4

3. M

ak

e a

pro

babil

ity h

isto

gra

m o

f th

e d

ata

.

0.8

0.6

0.4

0.2 0

0

P(X

)

X =

Nu

mb

er

of

Tim

es

Sp

inn

er

Lan

ds

on

Blu

e

Sp

inn

er

Pro

bab

ilit

yD

istr

ibu

tio

n

12

4. TELEC

OM

MU

NIC

ATIO

NS

U

se t

he t

able

th

at

show

s th

e p

robabil

ity d

istr

ibu

tion

of

the n

um

ber

of

tele

ph

on

es

per

stu

den

t’s

hou

seh

old

at

Wil

son

Hig

h.

a

. S

how

th

at

the d

istr

ibu

tion

is

vali

d.

0.0

1 +

0.1

6 +

0.3

4 +

0.3

9 +

0.1

0 =

1

b

. If

a s

tud

en

t is

ch

ose

n a

t ra

nd

om

, w

hat

is t

he p

robabil

ity t

hat

there

are

more

th

an

3

tele

ph

on

es

at

the s

tud

en

t’s

hom

e?

0.4

9

c.

Mak

e a

pro

babil

ity h

isto

gra

m o

f th

e d

ata

.

0.4

0.3

0.2

0.1 0

P(X

)

X =

Nu

mb

er

of

Tele

ph

on

es

per

Ho

use

ho

ld

Wil

so

n H

igh

Ho

useh

old

s

12

34

5

5. LA

ND

SC

APIN

G U

se t

he t

able

th

at

show

s th

e p

robabil

ity d

istr

ibu

tion

of

the n

um

ber

of

shru

bs

(rou

nd

ed

to t

he n

eare

st 5

0)

ord

ere

d b

y

corp

ora

te c

lien

ts o

f a l

an

dsc

ap

ing c

om

pan

y

over

the p

ast

fiv

e y

ears

.

a

. D

efi

ne a

ran

dom

vari

able

an

d l

ist

its

valu

es.

L

et

X =

th

e n

um

ber

of

sh

rub

s

ord

ere

d;

X =

50,

100,

150,

200,

250

b

. S

how

th

at

the d

istr

ibu

tion

is

vali

d.

0.1

1 +

0.2

4 +

0.4

5 +

0.1

6 +

0.0

4 =

1

c.

Wh

at

is t

he p

robabil

ity t

hat

a c

lien

t’s

(rou

nd

ed

) ord

er

was

at

least

150 s

hru

bs?

0.6

5

RED

WHITEBLUE

GREEN

YELLOW

X =

Nu

mb

er

of

Tele

ph

on

es

12

34

5+

Pro

bab

ilit

y0.0

10.1

60.3

40.3

90.1

0

X =

Nu

mb

er

of

Sh

rub

s50

100

150

200

250

Pro

bab

ilit

y0.1

10.2

40.4

50.1

60.0

4

Answers (Lesson 12-6)

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Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A19 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

40

Gle

ncoe A

lgeb

ra 1

12-6

Wo

rd

Pro

ble

m P

racti

ce

Pro

bab

ilit

y D

istr

ibu

tio

ns

1.G

AM

ES

A s

pin

ner

for

an

ad

ven

ture

gam

e d

ecid

es h

ow a

pla

yer

wil

l m

ove.

W

rite

th

e sa

mp

le s

pace

wit

h a

ll p

ossi

ble

ou

tcom

es i

f th

e sp

inn

er i

s sp

un

tw

ice.

F

F,

FB

, F

L,

FR

, B

F,

BB

, B

L,

BR

, L

F,

LB

, L

L,

LR

, R

F,

RB

, R

L,

RR

2. JO

BS

Th

e p

robabil

ity d

istr

ibu

tion

table

sh

ows

the

resu

lts

of a

new

spap

er s

urv

ey

that

ask

ed b

abysi

tter

s h

ow m

uch

th

ey

mak

e p

er h

our.

Ho

url

y P

ay

$3

$4

$5

$6

$7+

Pro

bab

ilit

y0.1

0.2

0.5

0.1

50.0

5

W

hat

is t

he

pro

babil

ity t

hat

a b

abysi

tter

ch

osen

at

ran

dom

fro

m t

he

surv

ey m

ak

es

mor

e th

an

$5 p

er h

our?

0.2

0 =

20

%

3. T

IME

Jam

es l

ook

s at

his

12-h

our

dig

ital

cloc

k w

hen

he

wak

es u

p i

n t

he

mid

dle

of

the

nig

ht.

Mak

e a p

robabil

ity

his

togra

m f

or a

ll o

f th

e p

ossi

ble

ou

tcom

es

if y

ou l

et X

equ

al

the

firs

t d

igit

of

the

tim

e. F

or i

nst

an

ce,

if i

t is

3:4

1,

the

firs

t d

igit

is

a 3

.

Pro

bab

ilit

y H

isto

gra

m

43

21

0.20

0.30

0.10 0

0.40

P (10)

0.50

56

78

9

X =

Fir

st d

igit

on

clo

ck

4.D

AR

TS

Su

pp

ose

two

dart

s are

th

row

n a

t a

trad

itio

nal

dart

boa

rd

an

d l

an

d n

ear

the

cen

ter,

bu

t n

ot o

n a

bu

llse

ye.

Wh

at

is t

he

pro

babil

ity t

hat

the

sum

of

thei

r sc

ores

is

less

th

an

or

equ

al

to 5

?

10

÷ 4

00 =

0.0

25 =

2.5

%

5.T

EN

NIS

All

sea

son

Oli

ver

’s t

enn

is c

oach

h

as

kep

t tr

ack

of

wh

ere

each

of

his

se

rves

has

lan

ded

du

rin

g p

ract

ice.

Th

e re

sult

s are

sh

own

in

th

e p

robabil

ity

dis

trib

uti

on t

able

. A

ser

ve

in r

egio

n 2

is

“in

”, w

hil

e a s

erve

in a

ny o

ther

reg

ion

is

a f

au

lt.

A s

erve

in r

egio

n 1

rep

rese

nts

h

itti

ng t

he

net

.

Reg

ion

12

34

5

Pro

bab

ilit

y0.1

90.5

20.1

50.0

90.0

5

a.

Wh

at

is t

he

pro

babil

ity t

hat

an

y o

ne

of O

liver

’s s

erves

doe

s n

ot h

it t

he

net

an

d i

s a f

au

lt?

0.2

9 o

r 29%

b.

Mak

e a p

robabil

ity h

isto

gra

m t

hat

rep

rese

nts

th

e d

ata

in

th

e ta

ble

.

Pro

bab

ilit

y H

isto

gra

m

43

21

0.20

0.30

0.10 0

0.40

P (x)

0.50

5

Reg

ion

Forw

ard

Left

Right

Backward

Lesson 12-6

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

41

Gle

ncoe A

lgeb

ra 1

12-6

Bin

om

ial

Dis

trib

uti

on

A b

inom

ial

dis

trib

uti

on i

s a p

art

icu

lar

typ

e of

pro

babil

ity d

istr

ibu

tion

. T

o d

eter

min

e a

pro

babil

ity a

bin

omia

l d

istr

ibu

tion

use

s th

e bin

omia

l co

effi

cien

ts a

nd

th

e fo

rmu

la

nC

k �

pk(1

- p

) n-

k w

her

e n

is

the

nu

mber

of

sele

ctio

ns,

k i

s th

e d

esir

ed o

utc

ome,

an

d p

is

the

pro

babil

ity o

f th

e d

esir

ed o

utc

ome.

So,

if

we

have

a b

ag t

hat

con

tain

s 4 r

ed b

all

s an

d 8

bla

ck b

all

s, w

e ca

n u

se t

his

for

mu

la t

o d

eter

min

e th

e p

robabil

ity o

f d

raw

ing e

xact

ly 2

red

ball

s ou

t of

5 d

raw

s if

we

retu

rn t

he

ball

aft

er e

ach

dra

w.

Use

th

e fo

rmu

la t

o d

eter

min

e th

e p

robabil

ity:

C(5

, 2) �

( 4 −

12 ) 2

(1 -

4 −

12 ) 3

= 8

0 −

243

So,

th

e p

robabil

ity o

f ch

oosi

ng e

xact

ly 2

red

ball

s ou

t of

5 d

raw

s is

80 −

243 .

Exercis

es

1. D

eter

min

e th

e p

robabil

ity o

f d

raw

ing e

xact

ly 3

bla

ck b

all

s.

80 −

243

2. C

omp

are

th

e p

robabil

ity f

oun

d i

n p

roble

m 1

to

the

pro

babil

ity f

oun

d i

n t

he

exam

ple

. E

xp

lain

wh

y t

hey

com

pare

th

e w

ay t

hey

do.

I

t is

th

e s

am

e a

s t

he e

xam

ple

becau

se t

he p

rob

ab

ilit

y o

f g

ett

ing

exactl

y

2 r

ed

balls i

s t

he s

am

e a

s t

he p

rob

ab

ilit

y o

f g

ett

ing

exactl

y 3

bla

ck b

alls.

3. D

eter

min

e th

e p

robabil

ity o

f d

raw

ing e

xact

ly 3

red

ball

s.

40 −

243

4. D

eter

min

e th

e p

robabil

ity o

f d

raw

ing e

xact

ly 4

red

ball

s.

10 −

243

5. N

ow a

ssu

me

that

ther

e are

3 r

ed b

all

s an

d 2

bla

ck b

all

s in

th

e E

ven

tP

rob

ab

ilit

y

P(0

Red)

8 −

125

P(1

Red)

36 −

125

P(2

Red)

54 −

125

P(3

Red)

27 −

125

bag.

Com

ple

te t

he

pro

babil

ity d

istr

ibu

tion

table

usi

ng t

he

bin

omia

l d

istr

ibu

tion

.

En

ric

hm

en

t

Answers (Lesson 12-6)

Page 19: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A20 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

42

Gle

ncoe A

lgeb

ra 1

12-6

Sp

read

sheet

Act

ivit

y

Pro

bab

ilit

y H

isto

gra

ms

U

se a

sp

rea

dsh

eet

to m

ak

e a

pro

ba

bil

ity

his

tog

ra

m f

or t

he n

um

ber

of

hea

ds w

hen

fiv

e c

oin

s a

re t

ossed

.

Ste

p 1

E

nte

r th

e n

um

bers

of

head

s, X

, in

to

Colu

mn

A.

Ste

p 2

U

se C

olu

mn

B t

o f

ind

th

e n

um

ber

of

ways

that

X h

ead

s ca

n b

e a

chie

ved

. If

a c

oin

is

toss

ed

5 t

imes,

X h

ead

s ca

n

be a

chie

ved

in

C(5

, X

) w

ays.

Ste

p 3

F

ind

th

e p

robabil

itie

s in

Colu

mn

C.

Ste

p 4

S

ele

ct C

olu

mn

C t

o c

reate

th

e

his

togra

m.

Ch

oose

Ch

art

fro

m t

he

Inse

rt m

en

u.

Th

en

Ch

oose

th

e

Colu

mn

ch

art

. U

se t

he S

eri

es

tab t

o

desi

gn

ate

th

e C

ate

gory

(X

) axis

labels

as

the d

ata

in

cell

s A

2 t

hro

ugh

A7.

Use

th

e m

en

us

to f

orm

at

the h

isto

gra

m.

Sp

read

sheets

have m

an

y f

orm

ula

s p

rogra

mm

ed

in

clu

din

g,

com

bin

ati

on

s an

d

perm

uta

tion

s, t

hat

can

be u

sed

to i

nvest

igate

pro

babil

ity.

A

2 3 4 5 6 7 81

BC

X =

Nu

mb

er

of

Head

s in

5 t

osses

Ways t

oA

ch

ieve

P (

x)

0.0

3125

0.1

5625

0.3

125

0.3

125

0.1

5625

0.0

3125

1 5

10

10 5 1

0 1 2 3 4 5

Sh

eet

1S

heet

2S

heet

3

Cell

B7 c

onta

ins

the f

orm

ula

CO

MB

IN(5

, 47).

Cell

C7 c

onta

ins

the f

orm

ula

B7/S

UM

(B2:B

7).

Exerc

ises

Fo

r E

xercis

es 1

–3,

use t

he p

ro

ba

bil

ity

his

tog

ra

m f

or t

ossin

g 5

co

ins.

1. W

hat

is t

he p

robabil

ity t

hat

more

th

an

3 h

ead

s are

toss

ed

? 0.1

875 o

r 18.7

5%

2. W

hat

is t

he p

robabil

ity t

hat

few

er

than

3 h

ead

s are

toss

ed

? 0.5

or

50%

3. Is

th

is a

vali

d p

robabil

ity d

istr

ibu

tion

? E

xp

lain

. Y

es;

each

pro

bab

ilit

y i

s g

reate

r

than

0 a

nd

less t

han

or

eq

ual

to 1

an

d t

he s

um

of

the p

rob

ab

ilit

ies i

s 1

.

4. U

se a

sp

read

sheet

to m

ak

e a

pro

babil

ity h

isto

gra

m f

or

the n

um

ber

of

head

s w

hen

ten

co

ins

are

toss

ed

. S

ee s

tud

en

ts’

wo

rk.

Exam

ple

Lesson 12-7

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

43

Gle

ncoe A

lgeb

ra 1

12-7

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n

Pro

bab

ilit

y S

imu

lati

on

s

Th

eo

reti

cal

an

d E

xp

eri

men

tal

Pro

bab

ilit

y

Th

e p

robabil

ity u

sed

to d

esc

ribe

even

ts m

ath

em

ati

call

y i

s ca

lled

th

eo

reti

ca

l p

ro

ba

bil

ity

. F

or

exam

ple

, th

e m

ath

em

ati

cal

pro

babil

ity o

f ro

llin

g a

4 w

ith

a n

um

ber

cube i

s 1

6 ,

or

P(4

) =

1

6 .

Ex

perim

en

tal

pro

ba

bil

ity

is t

he r

ati

o o

f th

e n

um

ber

of

tim

es

an

ou

tcom

e o

ccu

rs i

n a

n e

xp

eri

men

t to

th

e t

ota

l n

um

ber

of

even

ts o

r tr

ials

, k

now

n a

s th

e r

ela

tiv

e f

req

uen

cy

.

Exp

eri

men

tal

Pro

bab

ilit

y fr

equ

en

cy o

f an

ou

tcom

e

−−

tota

l n

um

ber

of

tria

ls

M

att

reco

rd

ed

th

at

it r

ain

ed

8 t

imes i

n N

ov

em

ber a

nd

sn

ow

ed

3 t

imes.

Th

e o

ther d

ay

s,

it w

as s

un

ny

. T

here a

re 3

0 d

ay

s i

n N

ov

em

ber.

Su

pp

ose

Ma

tt u

ses t

hese r

esu

lts t

o p

red

ict

No

vem

ber’s

wea

ther n

ex

t y

ea

r.

Wh

at

is t

he

pro

ba

bil

ity

th

at

a d

ay

in

No

vem

ber w

ill

be s

un

ny

?

Exp

eri

men

tal

Pro

babil

ity =

frequ

en

cy o

f ou

tcom

e

to

tal

nu

mber

of

tria

ls

=

(30 -

8 -

3)

30

=

19

30 =

63.3

%

Th

e p

robabil

ity t

hat

it w

ill

be s

un

ny o

n a

day i

n N

ovem

ber

is 6

3.3

%.

A

fo

otb

all

tea

m n

oti

ced

th

at

9 o

f th

e l

ast

20 c

oin

to

sses t

o c

ho

ose

wh

ich

tea

m w

ou

ld r

eceiv

e t

he b

all

fir

st

resu

lted

in

ta

ils.

Wh

at

is t

he e

xp

erim

en

tal

pro

ba

bil

ity

of

the c

oin

la

nd

ing

on

ta

ils? W

ha

t is

th

e t

heo

reti

ca

l p

ro

ba

bil

ity

?

Exp

eri

men

tal

Pro

babil

ity =

fr

equ

en

cy o

f ou

tcom

e

to

tal

nu

mber

of

tria

ls

=

nu

mber

of

tail

s

−−

tota

l n

um

ber

of

toss

ess

=

9

20 =

45%

In t

his

case

, th

e e

xp

eri

men

tal

pro

babil

ity t

hat

a c

oin

toss

wil

l be t

ail

s is

45%

. If

th

e c

oin

is

fair

, th

e m

ath

em

ati

cal

pro

babil

ity i

s 50%

.

Exerc

ises

1. D

IE R

OLL A

math

cla

ss d

eci

ded

to t

est

wh

eth

er

a d

ie i

s fa

ir,

that

is,

wh

eth

er

the e

xp

eri

men

tal

pro

babil

ity e

qu

als

th

e t

heore

tica

l p

robabil

ity.

Th

e r

esu

lts

for

100 r

oll

s are

sh

ow

n a

t th

e r

igh

t.

a

. W

hat

is t

he t

heore

tica

l p

robabil

ity o

f ro

llin

g a

6?

16.7

%

b.

Wh

at

is t

he e

xp

eri

men

tal

pro

babil

ity o

f ro

llin

g a

6?

47%

c.

Is t

he d

ie f

air

? E

xp

lain

you

r re

aso

nin

g.

Pro

bab

ly n

ot;

th

eo

reti

cal

pro

bab

ilit

y

≠ e

xp

eri

men

tal

pro

bab

ilit

y.

1:

1

2:

15

3:

4

4:

13

5:

15

6:

42

Exam

ple

1

Exam

ple

2

Answers (Lesson 12-6 and Lesson 12-7)

Page 20: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Answers

Co

pyri

gh

t ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f T

he M

cG

raw

-Hill C

om

pan

ies,

Inc.

Chapter 12 A21 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

44

Gle

ncoe A

lgeb

ra 1

12-7

Stu

dy

Gu

ide a

nd

In

terv

en

tio

n (c

on

tin

ued

)

Pro

bab

ilit

y S

imu

lati

on

s

Perf

orm

ing

Sim

ula

tio

ns

A m

eth

od

th

at

is o

ften

use

d t

o f

ind

exp

eri

men

tal

pro

babil

ity

is a

sim

ula

tio

n.

A s

imu

lati

on

all

ow

s you

to u

se o

bje

cts

to a

ct o

ut

an

even

t th

at

wou

ld b

e

dif

ficu

lt o

r im

pra

ctic

al

to p

erf

orm

.

In

on

e b

aseb

all

sea

so

n,

Pete

wa

s a

ble

to

get

a b

ase h

it 4

2 o

f th

e

254 t

imes h

e w

as a

t b

at.

a. W

ha

t co

uld

be u

sed

to

sim

ula

te h

is g

ett

ing

a b

ase h

it?

Fir

st f

ind

th

e e

xp

eri

men

tal

pro

babil

ity.

Exp

eri

men

tal

Pro

babil

ity =

fr

equ

en

cy o

f ou

tcom

e

to

tal

nu

mber

of

tria

ls

=

42

254 o

r 16.5

%

Noti

ce t

hat

the e

xp

eri

men

tal

pro

babil

ity i

s abou

t 1

6 .

Th

ere

fore

use

a

spin

ner

lik

e t

he o

ne a

t th

e r

igh

t w

ith

6 e

qu

all

y l

ikely

ou

tcom

es.

b. D

escrib

e a

wa

y t

o s

imu

late

his

nex

t 10 t

imes a

t b

at.

Let

an

ou

tcom

e o

f 1 c

orr

esp

on

d t

o P

ete

’s g

ett

ing a

base

hit

. L

et

all

oth

er

ou

tcom

es

corr

esp

on

d t

o h

is n

ot

gett

ing a

hit

. S

pin

th

e s

pin

ner

on

ce t

o s

imu

late

a t

ime a

t bat.

R

eco

rd t

he r

esu

lt a

nd

rep

eat

this

9 m

ore

tim

es.

Exerc

ises

1. G

UESSIN

G W

hat

cou

ld y

ou

use

to s

imu

late

th

e o

utc

om

e o

f gu

ess

ing o

n a

20 q

uest

ion

tru

e-f

als

e t

est

? S

am

ple

an

sw

er:

a c

oin

to

ssed

20 t

imes w

ith

head

s

co

rresp

on

din

g t

o t

rue a

nd

tails c

orr

esp

on

din

g t

o f

als

e

2. G

UESSIN

G W

hat

cou

ld y

ou

use

to s

imu

late

th

e o

utc

om

e o

f gu

ess

ing o

n a

20-q

uest

ion

m

ult

iple

ch

oic

e t

est

wit

h 4

alt

ern

ati

ve a

nsw

ers

labele

d A

, B

, C

, an

d D

for

each

qu

est

ion

?

Sam

ple

an

sw

er:

a s

pin

ner

wit

h 4

eq

ual-

siz

ed

secti

on

s l

ab

ele

d A

, B

, C

,

an

d D

sp

un

20 t

imes

3. PR

OM

OTIO

NS

M

ain

Str

eet

Su

perm

ark

et

ran

dom

ly g

ives

each

sh

op

per

a f

ree t

wo-l

iter

bott

le o

f co

la d

uri

ng t

he S

atu

rday s

hop

pin

g h

ou

rs.

Th

e s

up

erm

ark

et

sell

s 6 d

iffe

ren

t ty

pes

of

cola

.

a.

Wh

at

cou

ld b

e u

sed

to p

erf

orm

a s

imu

lati

on

of

this

sit

uati

on

? S

am

ple

an

sw

er:

a

sp

inn

er

wit

h 6

eq

ual-

siz

ed

secti

on

s lab

ele

d t

o r

ep

resen

t th

e 6

typ

es o

f

co

la

b.

How

cou

ld y

ou

use

th

is s

imu

lati

on

to m

od

el

the n

ext

50 b

ott

les

of

cola

giv

en

ou

t.

Sam

ple

an

sw

er:

sp

in t

he s

pin

ner

descri

bed

fo

r E

xerc

ise 3

fif

ty t

imes

4. PIC

NIC

S A

t a p

icn

ic,

there

were

2 p

ean

ut

bu

tter

san

dw

ich

es,

2 c

hic

ken

san

dw

ich

es,

a t

un

a s

an

dw

ich

, an

d a

tu

rkey s

an

dw

ich

in

a c

oole

r. D

esc

ribe a

sim

ula

tion

th

at

cou

ld

be u

sed

to f

ind

th

e p

robabil

ity o

f ra

nd

om

ly p

ick

ing a

cert

ain

san

dw

ich

fro

m t

he c

oole

r.

Sam

ple

an

sw

er:

If

rollin

g a

nu

mb

er

cu

be r

esu

lts i

n a

1 o

r 2,

ch

oo

se

pean

ut

bu

tter;

3 o

r 4,

ch

oo

se c

hic

ken

; 5,

ch

oo

se t

un

a;

6,

ch

oo

se t

urk

ey

12

54

36

Exam

ple

Lesson 12-7

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

45

Gle

ncoe A

lgeb

ra 1

12-7

Sk

ills

Pra

ctic

e

Pro

bab

ilit

y S

imu

lati

on

s

1. C

AR

DS

U

se a

sta

nd

ard

deck

of

52 c

ard

s. S

ele

ct a

card

at

ran

dom

, re

cord

th

e s

uit

of

the

card

(h

eart

, d

iam

on

d,

clu

b,

or

spad

e),

an

d t

hen

rep

lace

th

e c

ard

. R

ep

eat

this

pro

ced

ure

26 t

imes.

a

. B

ase

d o

n y

ou

r re

sult

s, w

hat

is t

he e

xp

eri

men

tal

pro

babil

ity o

f se

lect

ing a

heart

?A

nsw

ers

will

vary

. T

he t

heo

reti

cal

pro

bab

ilit

y i

s 0

.25.

b

. B

ase

d o

n y

ou

r re

sult

s, w

hat

is t

he e

xp

eri

men

tal

pro

babil

ity o

f se

lect

ing a

dia

mon

dor

a s

pad

e?

An

sw

ers

will

vary

. T

he t

heo

reti

cal

pro

bab

ilit

y i

s 0

.5.

c.

Com

pare

you

r re

sult

s to

th

e t

heore

tica

l p

robabil

itie

s. T

he t

heo

reti

cal

pro

bab

ilit

y

in p

art

a i

s 0

.25 a

nd

in

part

b i

s 0

.5.

2. SIB

LIN

GS

T

here

are

3 s

ibli

ngs

in t

he B

en

cieven

ga f

am

ily.

Wh

at

cou

ld y

ou

use

to

sim

ula

te t

he g

en

ders

of

the 3

sib

lin

gs?

S

am

ple

an

sw

er:

th

ree c

oin

s,

on

e f

or

each

of

the s

iblin

gs,

wit

h t

ails f

or

male

an

d h

ead

s f

or

fem

ale

, o

r 1 c

oin

tossed

th

ree t

imes

3. TR

AN

SPO

RTA

TIO

N A

ran

dom

su

rvey o

f 23 s

tud

en

ts r

eveale

d t

hat

2 s

tud

en

ts w

alk

to

sch

ool,

12 r

ide t

he b

us,

6 d

rive a

car,

an

d 3

rid

e w

ith

a p

are

nt

or

oth

er

ad

ult

. W

hat

cou

ld

you

use

for

a s

imu

lati

on

to d

ete

rmin

e t

he p

robabil

ity t

hat

a s

tud

en

t se

lect

ed

at

ran

dom

u

ses

an

y o

ne t

yp

e o

f tr

an

sport

ati

on

? S

am

ple

an

sw

er:

Use d

iffe

ren

tly c

olo

red

marb

les t

hat

matc

h i

n n

um

ber

wit

h t

he s

urv

ey f

or

each

tra

nsp

ort

ati

on

typ

e.

4. B

IOLO

GY

S

tep

hen

con

du

cted

a s

urv

ey o

f th

e s

tud

en

ts i

n h

is c

lass

es

to o

bse

rve t

he

dis

trib

uti

on

of

eye c

olo

r. T

he t

able

sh

ow

s th

e

resu

lts

of

his

su

rvey.

a

. F

ind

th

e e

xp

eri

men

tal

pro

babil

ity d

istr

ibu

tion

for

each

eye c

olo

r. P

(Blu

e) =

0.1

5,

P(B

row

n) =

0.7

25,

P(G

reen

) =

0.0

25,

P(H

azel)

= 0

.1

b

. B

ase

d o

n t

he s

urv

ey,

wh

at

is t

he e

xp

eri

men

tal

pro

babil

ity t

hat

a s

tud

en

t in

Ste

ph

en

’s

class

es

has

blu

e o

r gre

en

eyes?

0.1

75

c.

Base

d o

n t

he s

urv

ey,

wh

at

is t

he e

xp

eri

men

tal

pro

babil

ity t

hat

a s

tud

en

t in

Ste

ph

en

’s

class

es

does

not

have g

reen

or

hazel

eyes?

0.8

75

d

. If

th

e d

istr

ibu

tion

of

eye c

olo

r in

Ste

ph

en

’s g

rad

e i

s si

mil

ar

to t

he d

istr

ibu

tion

in

his

cl

ass

es,

abou

t h

ow

man

y o

f th

e 3

60 s

tud

en

ts i

n h

is g

rad

e w

ou

ld b

e e

xp

ect

ed

to h

ave

bro

wn

eyes?

ab

ou

t 261

Eye C

olo

rB

lue

Bro

wn

Gre

en

Hazel

Nu

mb

er

12

58

28

Answers (Lesson 12-7)

Page 21: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

Co

pyrig

ht ©

Gle

nco

e/M

cG

raw

-Hill, a

div

isio

n o

f Th

e M

cG

raw

-Hill C

om

pan

ies, In

c.

Chapter 12 A22 Glencoe Algebra 1

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

46

Gle

ncoe A

lgeb

ra 1

12-7

Practi

ce

Pro

bab

ilit

y S

imu

lati

on

s

1. M

AR

BLES

P

lace

5 r

ed

, 4 y

ell

ow

, an

d 7

gre

en

marb

les

in a

box.

Ran

dom

ly d

raw

tw

o

marb

les

from

th

e b

ox,

reco

rd e

ach

colo

r, a

nd

th

en

retu

rn t

he m

arb

les

to t

he b

ox.

Rep

eat

this

pro

ced

ure

50 t

imes.

a

. B

ase

d o

n y

ou

r re

sult

s, w

hat

is t

he e

xp

eri

men

tal

pro

babil

ity o

f se

lect

ing t

wo y

ell

ow

marb

les?

A

nsw

ers

will

vary

. T

he t

heo

reti

cal

pro

bab

ilit

y i

s 0

.05.

b

. B

ase

d o

n y

ou

r re

sult

s, w

hat

is t

he e

xp

eri

men

tal

pro

babil

ity o

f se

lect

ing a

gre

en

marb

le a

nd

a y

ell

ow

marb

le?

An

sw

ers

will

vary

. T

he t

heo

reti

cal

pro

bab

ilit

y

is a

bo

ut

0.2

33.

c.

Com

pare

you

r re

sult

s to

th

e t

heore

tica

l p

robabil

itie

s. T

he t

heo

reti

cal

pro

bab

ilit

y

in E

xerc

ise 1

is 0

.05,

an

d i

n E

xerc

ise 2

is a

bo

ut

0.2

33.

2. O

PTO

METR

Y C

olo

r bli

nd

ness

occ

urs

in

4%

of

the m

ale

pop

ula

tion

. W

hat

cou

ld y

ou

use

to s

imu

late

th

is s

itu

ati

on

? S

am

ple

an

sw

er:

a d

eck o

f p

layin

g c

ard

s i

n w

hic

h

1 c

ard

is r

ed

an

d 2

4 a

re b

lack

3. SC

HO

OL C

UR

RIC

ULU

M L

au

rel

Wood

s

Hig

h r

an

dom

ly s

ele

cted

stu

den

ts f

or

a

surv

ey t

o d

ete

rmin

e t

he m

ost

im

port

an

t

sch

ool

issu

es

am

on

g t

he s

tud

en

t bod

y.

Th

e s

chool

wan

ts t

o d

evelo

p a

cu

rric

ulu

m

that

ad

dre

sses

these

iss

ues.

Th

e s

urv

ey

resu

lts

are

sh

ow

n i

n t

he t

able

.

a

. F

ind

th

e e

xp

eri

men

tal

pro

babil

ity

dis

trib

uti

on

of

the i

mp

ort

an

ce o

f

each

iss

ue.

P(G

rad

es) ≈

0.1

19,

P(S

ch

oo

l S

tan

dard

s) ≈

0.0

55,

P(P

op

ula

rity

) ≈

0.2

70,

P(D

ati

ng

) ≈

0.2

44,

P(V

iole

nce) ≈

0.2

19,

P(D

rug

s) ≈

0.0

93

b

. B

ase

d o

n t

he s

urv

ey,

wh

at

is t

he e

xp

eri

men

tal

pro

babil

ity t

hat

a s

tud

en

t ch

ose

n a

t

ran

dom

th

ink

s th

e m

ost

im

port

an

t is

sue i

s gra

des

or

sch

ool

stan

dard

s? ab

ou

t 0.1

74

c.

Th

e e

nro

llm

en

t in

th

e 9

th a

nd

10th

gra

des

at

Lau

rel

Wood

s H

igh

is

168.

If t

heir

op

inio

ns

are

refl

ect

ive o

f th

ose

of

the s

chool

as

a w

hole

, h

ow

man

y o

f th

em

wou

ld y

ou

exp

ect

to h

ave c

hose

n p

op

ula

rity

as

the m

ost

im

port

an

t is

sue?

ab

ou

t 45

d

. S

up

pose

th

e s

chool

develo

ps

a c

urr

icu

lum

in

corp

ora

tin

g t

he t

op

th

ree i

ssu

es.

Wh

at

is

the p

robabil

ity t

hat

a s

tud

en

t se

lect

ed

at

ran

dom

wil

l th

ink

th

e c

urr

icu

lum

ad

dre

sses

the m

ost

im

port

an

t is

sue a

t sc

hool?

ab

ou

t 0.7

33

Sch

oo

l Is

su

es

Issu

eN

um

ber

Ran

kin

g

Issu

e M

ost

Imp

ort

an

t

Gra

des

37

School S

tandard

s17

Popula

rity

84

Dating

76

Vio

lence

68

Dru

gs,

inclu

din

g t

obacco

29

Lesson 12-7

Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.

NA

ME

DA

TE

PE

RIO

D

Ch

ap

ter

12

47

Gle

ncoe A

lgeb

ra 1

12-7

Wo

rd

Pro

ble

m P

racti

ce

Pro

bab

ilit

y S

imu

lati

on

s

1. G

AM

ES

S

up

pose

you

sp

in t

he s

pin

ner

belo

w 2

0 t

imes.

You

get

6 r

ed

, 4 b

lue,

5 y

ell

ow

, an

d 5

gre

en

. W

hat

is t

he

theore

tica

l p

robabil

ity o

f sp

inn

ing r

ed

?

Wh

at

is t

he e

xp

eri

men

tal

pro

babil

ity o

f

spin

nin

g r

ed

? 25%

; 30%

Red

Yellow

Blue

Green

2. EA

RTH

QU

AK

ES

G

eolo

gis

ts c

on

clu

de

that

there

is

a 6

2%

pro

babil

ity o

f a

magn

itu

de 6

.7 o

r gre

ate

r qu

ak

e s

trik

ing

the S

an

Fra

nci

sco B

ay r

egio

n b

efo

re

2032.

Does

this

rep

rese

nt

emp

iric

al

pro

ba

bil

ity,

theo

reti

cal

pro

ba

bil

ity,

or

exp

erim

enta

l p

roba

bil

ity?

em

pir

ical

3. TO

YS

T

here

is

a t

oy o

n t

he m

ark

et

that

is s

old

as

a m

oth

er

dog w

ith

her

pu

pp

ies.

Each

moth

er

dog c

om

es

wit

h 2

, 3,

or

4

pu

pp

ies.

Th

e n

um

ber

of

pu

pp

ies

in t

he

pack

age r

em

ain

s a s

urp

rise

un

til

the t

oy

is p

urc

hase

d a

nd

op

en

ed

. S

up

pose

th

e

toy c

om

pan

y h

as

state

d t

hat

on

e h

alf

of

the t

oy p

ack

ages

con

tain

2 p

up

pie

s, o

ne

thir

d o

f th

e p

ack

ages

con

tain

3 p

up

pie

s,

an

d o

ne s

ixth

of

the p

ack

ages

con

tain

4

pu

pp

ies.

Desc

ribe w

hat

cou

ld b

e u

sed

to

perf

orm

a s

imu

lati

on

for

dete

rmin

ing t

he

pro

babil

ity o

f ra

nd

om

ly r

ece

ivin

g a

cert

ain

nu

mber

of

pu

pp

ies.

Sam

ple

an

sw

er:

A

nu

mb

er

cu

be

co

uld

be u

sed

to

sim

ula

te t

he

ran

do

m e

ven

t o

f re

ceiv

ing

2,

3,

or

4 p

up

pie

s.

Let

#1-3

rep

resen

t

receiv

ing

2 p

up

pie

s;

let

#4 a

nd

5

rep

resen

t re

ceiv

ing

3 p

up

pie

s;

let

#6 r

ep

resen

t re

ceiv

ing

4 p

up

pie

s.

4. A

UTO

MO

BIL

ES

A

con

sum

er

gro

up

surv

eyed

its

mem

bers

an

d f

ou

nd

th

at

man

y o

f th

em

had

fla

ts o

r blo

wou

ts w

ith

a c

ert

ain

bra

nd

of

tire

. O

ut

of

a t

ota

l of

20,2

24 t

ires

pu

rch

ase

d,

984 d

evelo

ped

pro

ble

ms

wit

hin

th

e f

irst

1000 m

iles.

Lea

has

just

had

on

e o

f th

ese

tir

es

inst

all

ed

on

her

car.

Wh

at

is t

he p

robabil

ity t

hat

her

tire

wil

l h

ave a

fla

t or

blo

wou

t in

th

e

firs

t 1000 m

iles?

ab

ou

t 4.9

%

5. PO

LY

GR

APH

TESTIN

G A

form

er

FB

I

dete

ctiv

e h

as

develo

ped

a v

oic

e s

tress

an

aly

sis

devic

e t

o d

ete

rmin

e w

heth

er

or

not

a p

ers

on

is

tell

ing t

he t

ruth

. H

e

claim

s th

at

the d

evic

e i

s acc

ura

te 9

5%

of

the t

ime.

Ad

dit

ion

all

y,

a t

rad

itio

nal

poly

gra

ph

mach

ine h

as

a r

ep

ort

ed

acc

ura

cy r

ate

of

80%

.

a. S

up

pose

fou

r cr

imin

al

susp

ect

s are

giv

en

th

e v

oic

e s

tress

an

aly

sis.

Acc

ord

ing t

o t

he r

ep

ort

ed

em

pir

ical

pro

babil

ity,

wh

at

is t

he p

robabil

ity

that

the d

evic

e c

an

corr

ect

ly a

naly

ze

the a

ccu

racy

of

all

fou

r su

spect

s’

state

men

ts?

Rou

nd

you

r an

swer

to t

he

neare

st t

en

th o

f a p

erc

en

t.

81.5

%

b. If

a r

an

dom

ly c

hose

n p

ers

on

is

giv

en

both

th

e v

oic

e s

tress

an

aly

sis

an

d t

he

trad

itio

nal

poly

gra

ph

to v

ali

date

his

or

her

state

men

ts,

wh

at

is t

he p

robabil

ity

that

both

devic

es

are

able

to c

orr

ect

ly

dete

rmin

e t

he a

ccu

racy

of

the p

ers

on

’s

state

men

ts?

76%

Answers (Lesson 12-7)

Page 22: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company
Page 23: Answers (Lesson 12-1) - Mrs. Speer's Sitemrsspeer.weebly.com/uploads/4/9/7/1/4971042/algch12ans.pdfTo determine the popularity of online banking in the United States, a polling company

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