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 was 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 mph. Assume that the statistician also gave us the information that the distribution of serve speeds was mound-shaped and symmetric.
What percentage of the player's serves were between 115 mph and 145 mph?
A) at most 13.5%
B) approximately 16%
C) at most 2.5%
D) at most 34%

Question

Quizplus · Accepted Answer

The distribution is mound-shaped and symmetric, suggesting a normal distribution. The range 115 mph to 145 mph is one standard deviation above the mean (100 + 15 = 115) to three standard deviations above the mean (100 + 3*15 = 145). Approximately 16% of data in a normal distribution falls between one and three standard deviations above the mean.

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