At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 97 miles per hour (mph) and the standard deviation of the serve speeds was 13 mph. Assume that the statistician also gave us the information that the distribution of the serve speeds was mound-shaped and symmetric. What proportion of the player's serves was between 110 mph and 136 mph?
A) 0.1585
B) 0.997
C) 0.317
D) 136

Question

Quizplus · Accepted Answer

The z-score for 110 mph is (110 - 97) / 13 = 1.00. The z-score for 136 mph is (136 - 97) / 13 = 2.92. The proportion of the player's serves between 110 mph and 136 mph is the area under the normal curve between z = 1.00 and z = 2.92, which is 0.1585.

At the US Open Tennis Championship a Statistician Keeps Track of Every