Student Learning Outcomes The student will explore the properties of data through the Central Limit Theorem.

Given 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 size 12{X} {} be the random variable representing the time it takes her to complete one review. Assume X size 12{X} {} is normally distributed. Let X¯ size 12{ {overline {X}} } {} be the random variable representing the average time to complete the 16 reviews. Let ΣX size 12{ΣX} {} be the total time it takes Yoonie to complete all of the month’s reviews.

Distribution Complete the distributions. X ~ X ~ ΣX ~

Graphing Probability For each problem below: a Sketch the graph. Label and scale the horizontal axis. Shade the region corresponding to the probability.b Calculate the value. Find the probability that one review will take Yoonie from 3.5 to 4.25 hours. a b P( size 12{P \( } {} ________ <X< size 12{<X<} {} ________ )= size 12{ \) ={}} {} _______ b 3.5, 4.25, 0.2441 Find the probability that the average of a month’s reviews will take Yoonie from 3.5 to 4.25 hrs. a b P( )=_______ b 0.7499 Find the 95th percentile for the average time to complete one month’s reviews. a bThe 95th Percentile= b 4.49 hours Find the probability that the sum of the month’s reviews takes Yoonie from 60 to 65 hours. a b The Probability= b 0.3802 Find the 95th percentile for the sum of the month’s reviews.a b The 95th percentile= b 71.90

Discussion Question What causes the probabilities in and to differ?