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) approximately 16%
B) at most 13.5%
C) at most 2.5%
D) at most 34%

Question

Quizplus · Accepted Answer

The empirical rule states that for a mound-shaped and symmetric distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% of the data falls within two standard deviations of the mean, and 99.7% of the data falls within three standard deviations of the mean. In this case, the mean is 100 mph and the standard deviation is 15 mph. So, 68% of the serves are between 85 mph and 115 mph, 95% of the serves are between 70 mph and 130 mph, and 99.7% of the serves are between 55 mph and 145 mph. Therefore, the percentage of serves between 115 mph and 145 mph is approximately 16%.

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