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. If nothing is known about the shape of the distribution, what percentage of the player's serve speeds are less than 70 mph?
A) approximately 2.5%
B) at most 12.5%
C) at most 11%
D) at most 25%
E) approximately 5%

Question

Quizplus · Accepted Answer

Using Chebyshev's inequality, at least 75% of the data lies within 2 standard deviations from the mean, so at most 25% can be outside this range. Since 70 mph is 2 standard deviations below the mean, at most 25% of serves are less than 70 mph.

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