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 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 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: 50 mph, 80 mph, and 105 mph

A) 50 is the only outlier.
B) 50, 80, and 105 are all outliers.
C) 50 and 80 are both outliers, 105 is not.
D) None of the three speeds are outliers.

Question

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 100 miles per hour (mph) and the standard deviation of the serve speeds was 15 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: 50 mph, 80 mph, and 105 mph

Speeds: 50 mph, 80 mph, and 105 mph

A) 50 is the only outlier.
B) 50, 80, and 105 are all outliers.
C) 50 and 80 are both outliers, 105 is not.
D) None of the three speeds are outliers.

Quizplus · Accepted Answer

A z-score is calculated as (X - mean) / standard deviation. A common rule is that a z-score beyond ±2 or ±3 indicates an outlier. For 50 mph, the z-score is (50-100)/15 = -3.33, which is an outlier. For 80 mph, the z-score is (80-100)/15 = -1.33, and for 105 mph, it is (105-100)/15 = 0.33. Neither 80 mph nor 105 mph have z-scores beyond ±2, so they are not outliers.

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