Yoonie is a personnel manager in a large corporation. Each month she must review 15 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let Xhe the random variable representing the time it takes her to complete one review. Assume X is normally distributed. Let} be the random variable representing the mean lime to complete the 15 reviews. Assume that the 16 reviews represent a random set of reviews. Find the 95th percentile for the mean time to complete one month's reviews. (a) Sketch the graph. AA )7; O 46 i 3.1 3.4- 3.7 4 4.3 . 4.9 O 3.1 3.4- 3.7 4 4.3 4.6 4.9 A X i O 3.1 3.4- 3.7 4 4.3 4.6 4.9 O 3.1 3.4- 3.7 4 4.3 4.6 4.9 (b) Give the 95tl1 Percentile. (Round your answer to two decimal places.) |:| Yoonie is a personnel manager in a large corporation. Each month she must review 15 of the employees. From past experience, she has found that the reviews take her approximately four hours each to do with a population standard deviation of 1.2 hours. Let Xbe the random variable representing the time it takes her to complete one review. Assume Xis normally distributed. Let} be the random variable representing the mean time to complete the 15 reviews. Assume that the 16 reviews represent a random set of reviews. Find the probability that the mean of a month's reviews will take Yoonie from 3.5 to 4.25 hrs. (a) Sketch the graph, labeling and scaling the horizontal axis. Shade the region corresponding to the probability. MI NI 0.4 1.6 2.8 4 5.2 6.4 7.6 O 0.4 1.6 2.8 4 5.2 6.4 7.6 MI Ni O 0.4 1.6 2.8 4 5-2 6.4 7.6 O 0.4 1.6 2.8 4 5.2 6.4 7.6 X (b) Give the probability statement and the probability. (Enter exact numbers as integers, fractions, or decimals for the probability statement. Round the probability to four decimal places.) 90 |