Name: Class: Date: (First Page) Name: Class: Date: (Subsequent Pages) 1. {Exercise 5.07}

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1 Name: Class: Date: _ (First Page) Name: Class: Date: _ (Subsequent Pages) 1. {Exercise 5.07} The probability distribution for the random variable x follows. Excel File: data05 07.xls a. f(x) is greater than 0 for all x. Is this a valid probability distribution? _ b. What is the probability that x = 30? c. What is the probability that x is less than or equal to 25? d. What is the probability that x is greater than 30? printing/ /html print?sel= /8

2 2. {Exercise 5.09} For unemployed persons in the United States, the average number of months of unemployment at the end of December 2009 was approximately seven months (Bureau of Labor Statistics, January 2010). Suppose the following data are for a particular region in upstate New York. The values in the first column show the number of months unemployed and the values in the second column show the corresponding number of unemployed persons. Excel File: data05 09.xls Let x be a random variable indicating the number of months a person is unemployed. a. Use the data to develop an empirical discrete probability distribution for x (to 4 decimals). (x) f(x) b. Show that your probability distribution satisfies the conditions for a valid discrete probability distribution. printing/ /html print?sel= /8

3 The input in the box below will not be graded, but may be reviewed and considered by your instructor. _ c. What is the probability that a person is unemployed for two months or less (to 4 decimals)? Unemployed for more than two months (to 4 decimals)? d. What is the probability that a person is unemployed for more than six months (to 4 decimals)? printing/ /html print?sel= /8

4 3. {Exercise 5.17} The number of students taking the SAT has risen to an all time high of more than 1.5 million (College Board, August 26, 2008). Students are allowed to repeat the test in hopes of improving the score that is sent to college and university admission offices. The number of times the SAT was taken and the number of students are as follows. Excel File: data05 17.xls a. Let x be a random variable indicating the number of times a student takes the SAT. Show the probability distribution for this random variable (to 4 decimals). x = 1 _ x = 2 _ x = 3 _ x = 4 _ x = 5 _ b. What is the probability that a student takes the SAT more than one time (to 4 decimals)? _ c. What is the probability that a student takes the SAT three or more times (to 4 decimals)? _ d. What is the expected value of the number of times the SAT is taken (to 4 decimals)? _ What is your interpretation of the expected value? The input in the box below will not be graded, but may be reviewed and considered by your instructor. _ e. What is the variance and standard deviation for the number of times the SAT is taken (to 4 decimals)? printing/ /html print?sel= /8

5 Variance _ Standard deviation _ 4. {Exercise 5.19} The National Basketball Association (NBA) records a variety of statistics for each team. Two of these statistics are the percentage of field goals made by the team and the percentage of three point shots made by the team. For a portion of the 2004 season, the shooting records of the 29 teams in the NBA showed the probability of scoring two points by making a field goal was.44, and the probability of scoring three points by making a three point shot was.34 ( January 3, 2004). a. What is the expected value of a two point shot for these teams (to 2 decimals)? b. What is the expected value of a three point shot for these teams (to 2 decimals)? c. If the probability of making a two point shot is greater than the probability of making a three point shot, why do coaches allow some players to shoot the three point shot if they have the opportunity? _ printing/ /html print?sel= /8

6 5. {Exercise 5.33} Consider a binomial experiment with n = 20 and p =.70. a. Compute f(12) (to 4 decimals). b. Compute f(16) (to 4 decimals). c. Compute P(x 16) (to 4 decimals). d. Compute P(x 15) (to 4 decimals). e. Compute E(x). f. Compute Var(x) (to 1 decimal) and σ (to 2 decimals). Var(x) σ _ printing/ /html print?sel= /8

7 6. {Exercise 5.39} Twelve of the top 20 finishers in the 2009 PGA Championship at Hazeltine National Golf Club in Chaska, Minnesota, used a Titleist brand golf ball (GolfBallTest website, November 12, 2009). Suppose these results are representative of the probability that a randomly selected PGA Tour player uses a Titleist brand golf ball. For a sample of 15 PGA Tour players, make the following calculations. a. Compute the probability that exactly 10 of the 15 PGATour players use a Titleist brand golf ball (to 4 decimals). _ b. Compute the probability that more than 10 of the 15 PGA Tour players use a Titleist brand golf ball (to 4 decimals). _ c. For a sample of 15 PGA Tour players, compute the expected number of players who use a Titleist brand golf ball. _ d. For a sample of 15 PGATour players, compute the standard deviation of the number of players who use a Titleist brand golf ball (to 4 decimals). _ 7. {Exercise 5.41 (Algorithmic)} A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. a. Compute the probability that 2 or fewer will withdraw (to 4 decimals). b. Compute the probability that exactly 4 will withdraw (to 4 decimals). c. Compute the probability that more than 3 will withdraw (to 4 decimals). d. Compute the expected number of withdrawals. printing/ /html print?sel= /8

8 8. {Exercise 5.43} Twenty three percent of automobiles are not covered by insurance (CNN, February 23, 2006). On a particular weekend, 35 automobiles are involved in traffic accidents. a. What is the expected number of these automobiles that are not covered by insurance (to the nearest whole number)? b. What is the variance (to 1 decimals) and standard deviation (to 2 decimals)? Variance Standard deviation PAGE 1 (First Page) PAGE 1 (Subsequent Pages) printing/ /html print?sel= /8