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 96 miles per hour (mph)and the standard deviation of the serve speeds was 9 mph. Using the
Z-score approach for detecting outliers, which of the following serve speeds would represent
Outliers in the distribution of the playerʹs serve speeds?
Speeds: 65 mph, 105 mph, and 114 mph
A)None of the three speeds is an outlier.
B)65 and 105 are both outliers, but 114 is not.
C)65 is the only outlier.
D)65, 105, and 114 are all outliers.

Question

Quizplus · Accepted Answer

65 is the only outlier. To determine outliers using the Z-score approach, we calculate the Z-score for each serve speed: Z = (X - mean) / standard deviation. For a serve speed to be considered an outlier, its Z-score typically needs to be less than -3 or greater than 3. For 65 mph: Z = (65 - 96) / 9 = -31 / 9 ≈ -3.44, which is less than -3, making it an outlier. For 105 mph: Z = (105 - 96) / 9 = 9 / 9 = 1, not an outlier. For 114 mph: Z = (114 - 96) / 9 = 18 / 9 = 2, also not an outlier.

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