Question

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 four 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 X be the random variable representing the mean time to complete the 16 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.

(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.)

P 

  < x <  

=

Answer 1

(a)

Following is the graph:

(b)

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