1. 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. X1357 P(X).2.3.4.1 Y510 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 = __________

2. 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+Y68101211131517 P(X+Y).08.12.16.04.12.18.24.06

3. 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)

4. 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?

5. 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?

6. 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? X0123456 P(X)

7. 11.Lets assume based on previous years that the probability that is snows on December 25 th 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 25 th five or more days in the future? Can you use your calculator to complete this chart? X123456 P(X)

8. 14. A a.What is the value of A so the density curve is valid? b.P(x<0.4) = c.Where is Q3?

9. 1985 2000 pounds 1995 33,900 pounds 1986 4000 pounds 1996 21,000 pounds 1987 6000 pounds 1997 18,810 pounds 1988 7600 pounds 1998 17,039 pounds 1989 8500 pounds 1999 20,787 pounds 1990 16,000 pounds 2000 20,202 pounds 1991 19,000 pounds 2001 24,276 pounds 1992 20,780 pounds 2002 23,059 pounds 1993 23,373 pounds 2003 30,215 pounds 1994 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?