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Question: Sports and Leisure. One measure of an athlete's ability is the height of his or her vertical leap. Many professional basketball players are known for their remarkable vertical leaps, which lead to amazing dunks. DJ Stephens is the current vertical-leap record holder at 46 inches. However, the mean vertical leap of all NBA players is 28 inches. Suppose the standard deviation is 7 inches and 36 NBA players are selected at random.

a. What is the probability that the mean vertical leap for the 36 players will be less than 26 inches?

b. What is the probability that the mean vertical leap for the 36 players will be between 27.5 and 28.5 inches?

c. A high-priced athletic trainer has been hired to work with a group of NBA players to improve their hip flexibility, which should improve their vertical leap. After one month of training, the mean vertical leap for 50 of these players selected at random was 29.75 inches. Is there any evidence to suggest this flexibility program has increased the mean vertical leap (from μ = 28 inches)?

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