r AP StatisticsTest Ch 6,7 REVIEW

(a) 0.5(b) 0.75

/ralilo.szsVt

(e) 1.2s

Name

Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.

1. Family size can be represented by the random variable X. Determine the average family size.

@) 2.ea

GD\3'00

6j.;; . 2(v) v 3C\r) r't('zo) * . (.'o) = z x'eG)w1,Aq(e) 3.86

2. Suppose the average height of policemen is 71 inches with a standard deviation of 4 inches, while the average for policewoman is

66 inches with a standard deviation of 3 inches. If a committee looks at all ways of pairing up one male with one female officer, whatwill be the mean and standard deviation for the difference.in he.igtr]!! {or the set of possible partners?

-

(a) Mean of 5 inches with a standard deviation of I inch. \v .Jouq, erjolfo.c,trn0\+, b g*nc)ornrLr r"J.'"^s /4l Mean of 5 inches with a standard deviation of 3.5 inches ' !)

fZ6ilV""n of 5 inches with a standard deviation of 5 inches. /r^-r*oo -- &,ror. - &uto*,"= 7l - tao = 5V U"un of 68.5 inches with a standard deviation of 1 inch.

(e) Mean of 68.5 inches with a standard deviation of 3.5 inches "i"*-

do$,,n = Jfr."^ + cr?rorr*". = (tf* (3f : 2b

\ruto.tyts I

3. My wife's friend, Karen, and her husband really want to have a baby girl. Because of financial consideratiols, they decide theywill have children either until the.v have a girl or a total o-f 3 children if the probability of having a boy or girl is equally likely,determine the expected number of boys. [...piease note, as soon as they have a girl, they stop having kidsl Draw a tree diagram!]

(:

+

erd.l

,JioC \-'"r7t4. Which of the following are true statements?

l./ , By the law of large numbers, the mean of a random variable will get closer and closer to a specific value

L { The standard deviation ofa random variable is never negative.

1II."t The standard deviation ofa random variable is 0 only ifthe random variable takes a lone single value.

I and III and IIIII and III

G .5zr{oboi6

(a)

(b)(c)

,24c^J

X 2 J 4 5

Pfi) 17 .41 .26 .10

(d) II and III

@t,II, andlII

c5. IfP(X) : 0.23 and P(X and Y) : 0.12 -d 3G,orY)a4, find P(Y ).

[I would draw a.Venn Diagram if FweT6ffi

(a) 0.23(b) 0.52

ffi;;

*\o*t dtcr,tJi\ .

-{^e or}(J l4'rs . 12 So :g or.olcth,.t ir .

- *trg !^.,V"tg X b"\,b\t ntrJs{"bo . zB(S,,Utr".1 ro 6et

r{rc .\\ on-Vrc ktf ).- 13nr5t*4, crtn, r,*i,00 erttrpt b*blu

ir .at (ait'frictttr. .i1^"i.:1 *).-stf, {rtnr, -t\ oa *h+ n$t I

-6's(t)=e (r') " ^17

Use the following information for questions 6-8.

distribution tables.

The independent random variables X and Y are defined by the following probability

8e6* {, = 3.21

'P^ffi; the mean orx+Y

\#s+i.j s.r 4*n, . &x * &y(d) e ^'l .- 2.i+E.l(e) 4.3

7. Determine the standard deviation of 3Y + 5(a) .44(b) 3.62(c) o(a 5.1

ft,i\s.qc -- 3c-v(

Sterh \hs J s{r'hhan o+\ 3 .

+rigus '\h{, crl

&<t.lo i! owc 5<=:

)oes nolh,nqV c, /1 vo.rct- t ot cN""";rn*t "-,J*',,nb*oQN

\,

: 2.\ ti-: t.51?Q? &" t Z..l 6-: r ,4.

x 'l 3 6 Y 2 J 5 1

P(X) .6 .3 I P(v) I .2 .J .4

7. Which of the following is p! true concerning discrete probability distribution?

(a) The probability of any specific value is between 0 and 1, inclusive.

(b) The mean of the distribution is between the smallest and largest value in the distribution.

LQ The sum of allprobabilities is l.

PTH:tltfJffiifi ."i,',i'fJ:xf Jff i;.Hff ,L-ff:il*--6w&u*f;;ff*ff "PETg. The amount of pollutants a factory dumps into a river is approximately normally distributed with a mean of 2.43 and a standard

deviation of 0.88 tons. What is the probability that it dumps more than 3 tons?

9. lf arandomly selected person from this table is wealthy, what is the probability he or she is a Republican?

\pondt(i.',n.w\r o r.lormn{, d't{rrbvtrur" logs$- \tshoo\\R hlN" ?U lNu*o.r-du6 gg candok'tal*,b\r,s 1; \)

P [rs) = p C r gA ' tC> o.onf = norrwJ<J( (e", ito)Ranrrhlicar: reyvr

l4z^ -,Wealthy 87 72 J5

-ffit-Wealtf, 418 501 90 t

5o\ 617%

tzj r?or

@llll'.ffi;,"lD) u.z6+J ,QC*r,..(c) 0.6500 doottttr'ial o.ztsz \*t111ts(e) 0.7422 ''T"'

Riti?(c) 0.1s99(d) 0.8401(e) I thought all Republicans were wealthy.

t0.

Part II - Free Response (Questions ll-12) - Show your work and explain your results clearly.

Suppose the probabiiity that someone will make a major mistake on an income tax return is 0.2. An Internal RevenueService (IRS) agent plans to audit twenty returns and determine how many had a major mistake.

a. Define an appropriate assignment of random digits and using the given random number table, simulate (and clearlylabel) this situation 4 times.

75592 08563 79140 924s42o hos i nil6Ffcr. 2al 20 yoa 3 m.s{otrs

53645 66812 6t421 47836 2609 15373 98481 14s92

:8. t,t q,$ o,t -- rnrslak^- @Z.cl"^.-)dtttt L-1 = 1o m.r{alcr-ffoZ. .r*,-;

3rd bto.kot 2o hrl 3rnclakes

b. Based on your results, what is the expected number of returns with a major mistake?

x'jJ%-' t = gt!Yt?i*.*-

tl.lr+ri.,t,(?-o hmfrnrrtek+S

a

08424 44753 77377 28744

I 1. Airlines routinely overbook flights because they expect a certain number of no-shows. An airline runs a 5 p.m. commuterflight from Washington, D.C. to New York City on a plane that holds 38 passengers. Past experience has shown that if 4ltickets are sold for the flight, then the probability distribution for the number who actually show up for the flight is as shownin the table below.

Sqn*,t ,{q.."6 3gtosll 2**t flP*,rr /^y9,# tSYV/rnoqroiD!'

O^g-tosAssume that 4l tickets are sold for each flight.

a. There are 38 passenger seats on the flight.will get a seat?

wh"t i,ffilllh$Xf"ssensers who show up ror this night

What is the expected number of no-shows for this flight?

e(gu*)i*o '? 'rro '05 'ot'o\= q.t *?u?1.\*

Number who

Probabiiitv

ts are filled on a what is the only 36 passengers showed up

12. Ap Statistics test scores on Random Variables are described by the following probability distribution.

Score : * 40 50 60 t0 80

P(Score) 0.1 0.2 0.3 0.3 0.1

(a) Determine the

( - trrrrtt rx -- ".att8)

Mr. Custer, in yet another act of benevolence, decides to scale the scores so his students will not be denied admission to the

college of theii choice. He decides the actual grades will become: Grade: 1'5 * Score - 20 '

d4*"$q'5(i) Determine the mean and variance of the Grades z Ao c-lrunq^

(b)

&rr*-2o = t'5 1t - *)"/ /nocJ,\anq&,{ ,/ i.lunw"tubtra.}Zo

cI -..

" Ilr,i, :6, er^ " .ii";[ W^-J ,q.y% !ffi-\(ii) Which Score(s), if any, did not increase? ( \

r r, u ,, -^L . U - .l-^- ^^An^,4rr-r^ulO -stsf-J

-{(.. sarq-,-trhrool\+t^-+o s{"^tL!,lt*t'o {cst \{tc;ea>&Nl )

(c) Suppo.se three Scores were randomly (and lry!ggg$!!) selected'

(i) Determine the mean and variance of the total of the three Scores.

G. zn't)

$:z .OOJ

^ ,OA7

: .Og|

I

\

4"w'- h**\.X3 G\t6\rbl = \63

o{gr' fi**rr*r= l4+t4+tz1' 6t/

(ii) What is the probability that the average of the three scores is greater than 7 5?

No\f,ftur.s o*; ^.

cot\, -*J* J* a tt+&- rn a^+ 6fl;lt otr 76. , . Q",fi;{33$}['.lt)

1ffi **J *J lu

tnl 1 -t\ ^/'n'qn 75 orrv\aco

e\\ A scoc{S80 c*'rD

2*o.l'lT9-lficcr-e.7o

on\^r on{, \rJo{ bl\rupgo* I 1

6

T

?

P

'*hrlc."tt

if**7 76) = .or6d\