AP Statistics: Chapter 7 Review. Let X represent the number of present Mr. Cazzato will receive this holiday from Mrs. Cazzato. Let Y represent the number of presents Mrs. Cazzato will receive from Mr. Cazzato this holiday. The following represent two independent random variable distributions.

X 1 3 5 7

P(X) .2 .3 .4 .1

Y 5 10

P(Y) .4 .6

1. Calculate the mean, variance, and standard deviation of each random variable.

Mean X = ________ Mean Y = __________

Var X = ________ Var Y = __________

Stddev X = ________ Stddev Y = __________

The table below represents the distribution of X + Y.

2. Do you understand how this table was created? 3. Do you understand what this table represents?

4. Calculate the mean, variance, and standard deviation of the random variable X + Y.

Mean X + Y = ________

Var X + Y = ________

Stddev X + Y = ________

X+Y 6 8 10 12 11 13 15 17

P(X+Y) .08 .12 .16 .04 .12 .18 .24 .06

If needed, you can complete this table to help you. But it is not necessary.

6. Calculate the mean, variance, and standard deviation of the random variable X - Y.

Mean X - Y = ________

Var X - Y = ________

Stddev X - Y = ________

X-Y

P(X-Y)

7. Lets assume that the time Santa Clause spends at a household of a family of three is normally distributed with a mean of thirteen minutes and a standard deviation of one and a half minutes. What is the probability that Santa Clause spends more than twelve minutes at the house?

8. Lets assume that the time Santa Clause spends at a household of a family of five is normally distributed with a mean of seventeen minutes and a standard deviation of two minutes. What is the probability that Santa Clause spends between fourteen and seventeen and a half minutes at the house?

9. Using problem 7 and 8, what is the mean and standard deviation of the difference in time Santa spends at a house of family of five and a family of three?

10. What is the probability that Santa spends more time at the household of a family of three?

11. Lets assume that the number of presents Rick Jr. receives from his immediate family is a binomial distribution with the probability that one buys him a present is 0.6. Complete the chart below. X represents the number of presents.

a. What is the probability that Rick Jr. receives four presents?

b. What is the probability that Rick Jr. receives more than four or more presents?

c. What is the mean and standard deviation?

Can you use your calculator to complete this chart?

X 0 1 2 3 4 5 6

P(X)

11. Lets assume based on previous years that the probability that is snows on December 25th is 0.3. What is the probability that the next time snow falls on this day will be in the year 2012?

12. Using number 11, what is the mean number of years before it snows?

13. Using number 11, what is the probability that it snows on December 25th five or more days in the future?

Can you use your calculator to complete this chart?

X 1 2 3 4 5 6

P(X)

14.

Density Curve

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.2 0.4 0.6 0.8 1

x

y

A

a. What is the value of A so the density curve is valid?

b. P(x<0.4) =

c. Where is Q3?

1985     2000 pounds                 1995     33,900 pounds1986     4000 pounds                 1996     21,000 pounds1987     6000 pounds                 1997     18,810 pounds1988     7600 pounds                 1998     17,039 pounds1989     8500 pounds                 1999     20,787 pounds1990     16,000 pounds              2000     20,202 pounds1991     19,000 pounds              2001     24,276 pounds1992     20,780 pounds              2002     23,059  pounds1993     23,373 pounds              2003     30,215  pounds1994     30,443 pounds              2004     24,000 pounds

Food Drive Data

15. Is the data the number of pounds of food normally distributed?If yes, what is the probability that we meet our goal of 20,000 pounds?

No

rma

l Q

ua

nti

le

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

pounds0 10000 20000 30000

Collection 1 Normal Quantile Plot

pounds0 10000 20000 30000

Collection 1 Box Plot

Summary TableCollection 1

pounds18549.2

8917.7441

S1 = meanS2 = stdDev