Solution and Answer Guide: Camm/Cochran/Fry/Ohlmann/Anderson/Sweeney/Williams, Essentials of Statistics for Business and Economics, 10e 9780357716014; Chapter 6: Continuous Probability Distributions Solutions: a. Mean time between arrivals = 1/7 minutes b. f (x) = 7e−7x c. P(x > 1) = 1 − P(x < 1) = 1 − [1 − e−7(1)] = e−7 = 0.0009 d. 12 seconds is 0.2 minutes P(x > 0.2) = 1 − P(x < 0.2) = 1 − [1 − e−7(0.2)] = e−1.4 = 0.2466 53. Waiting in Line at Kroger. Supermarket chain Kroger has used computer simulation and information technology to reduce the average waiting time for customers at 2300 stores. Using a new system called QueVision, which allows Kroger to better predict when shoppers will be checking out, the company was able to decrease average customer waiting time to just 26 seconds (InformationWeek website). LO 8 a. Assume that Kroger waiting times are exponentially distributed. Show the probability density function of waiting time at Kroger. b. What is the probability that a customer will have to wait between 15 and 30 seconds? c. What is the probability that a customer will have to wait more than 2 minutes? Solutions: a. f (x) = 1  1 e −x/ = e−x/26 for x > 0 26 b. P(x < x0) = 1− e−x /  0 P(x < 30) = 1− e−30/26 = 1 − 0.3154 = 0.6846 P(x < 15) = 1− e−15/26 = 1 − 0.5932 = 0.4384 P(15 < x < 30) = P(x < 30) − P(x < 15) = 0.6846 − 0.4384 = 0.2462 c. P(x > 120) = 1 − P(x < 120) = 1− (1− e−120/ 26 ) = e−120/ 26 = 0.0099 There is less than a 1% chance of waiting more than two minutes. 54. Calls to Insurance Claims Office. The time (in minutes) between telephone calls at an insurance claims office has the following exponential probability distribution. LO 8, 9 f (x ) = 0.50e−0.50 x for x  0 a. What is the mean time between telephone calls? b. What is the probability of having 30 seconds or less between telephone calls? c. What is the probability of having 1 minute or less between telephone calls? d. What is the probability of having 5 or more minutes without a telephone call? Solutions: 1 a. = 0.5 therefore μ = 2 minutes = mean time between telephone calls  b. Note: 30 seconds = 0.5 minutes P(x ≤ 0.5) = 1 − e−.5/2 = 1 − 0.7788 = 0.2212 c. P(x ≤ 1) = 1 − e−1/2 = 1 − 0.6065 = 0.3935 d. P(x ≥ 5) = 1 − P(x < 5) = 1 − (1 − e−5/2) = 0.0821 55. Laffy Taffy Candy Production. Laffy Taffy is a type of taffy candy made from corn syrup, sugar, palm oil, and other ingredients. Laffy Taffy comes in a variety of flavors including strawberry, banana, and © 2024 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. 321