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Yoonie is a personnel manager in a large corporation. Each month she must review 16 of the employees. From past experience, she has found that the reviews take her approximately 4 hours each to do with a population standard deviation of 1.2 hours. Let $X$ be the random variable representing the time it takes her to complete one review. Assume $X$ is normally distributed. Let $\overline{X}$ be the random variable representing the average time to complete the 16 reviews. Let $\mathrm{\Sigma X}$ be the total time it takes Yoonie to complete all of the month’s reviews.
Complete the distributions.
For each problem below:
Find the probability that one review will take Yoonie from 3.5 to 4.25 hours.
Find the probability that the average of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs.
Find the 95th percentile for the average time to complete one month’s reviews.
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