Questions 4-5 ( about Melanie Kildare ) below refer to the Central Limit Theorem for Sample Means (Averages )

Melanie Kildare, daughter of Dr. James Kildare, is the nursing personnel manager at Blair General Hospital in Grand Rapids. Each month she must review 18 of the employees. From past experience, she has found that the reviews take her approximately three (3) hours each to do with a population standard deviation of 1.3 hours. Let X be 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 time to complete the 18 reviews. Assume that the 18 reviews represent a random set of reviews.

4)Find the probability, P ( ), that the mean of a month's reviews will take Melanie from 2.75 to 4.0 hrs. Sketch the graph, labeling and scaling the horizontal axis. Shade the interval area corresponding to the probability.

a. ( shade the diagram appropriately )

b. P(___________) = ________

5)Find the 95^th percentile for the mean time to complete one month's reviews. Sketch the graph.

a.( shade the diagram up to the 95^th percentile )

b.The 95^th Percentile =_______