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 103 miles per hour (mph) and the standard deviation of the serve speeds was 12 mph. Using the z-score approach for detecting outliers, which of the following serve speeds would represent outliers in the distribution of the player's serve speeds? Speeds: 61 mph, 115 mph, and 127 mph
A) 61 is the only outlier.
B) 61 and 115 are both outliers, but 127 is not.
C) 61, 115, and 127 are all outliers.
D) None of the three speeds is an outlier.

Question

Quizplus · Accepted Answer

A serve speed is considered an outlier if its z-score is less than -3 or greater than 3. The z-score for 61 mph is (61-103)/12 = -3.5, which is an outlier. The z-scores for 115 mph and 127 mph are within the range of -3 to 3, so they are not outliers.

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