Motivation of athletes. A statistician keeps track of every serve that a player hits during the U.S. Open Tennis Championship. The statistician reports that the mean serve speed was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph.

a. Suppose the statistician also observes that the distribution of serve speeds was mound-shaped and symmetric. What percentage of the player’s serves was between 115 mph and 145 mph?

b. Consider the following serve speeds: 50 mph, 80 mph, and 105 mph. Using the z-score approach for detecting outliers, which of these would represent outliers in the distribution of the player’s serve speeds?

c. If nothing is known about the shape of the distribution, what percentage of the player’s serve speeds are less than 70 mph?