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

Question

Quizplus · Accepted Answer

The z-score is calculated by subtracting the mean from the observation and then dividing by the standard deviation. An outlier is typically considered to be any value that has a z-score less than -3 or greater than 3. For the given speeds: - 50 mph: z = (50 - 100) / 15 = -50 / 15 = -3.33, which is less than -3, making it an outlier. - 80 mph: z = (80 - 100) / 15 = -20 / 15 = -1.33, which is not less than -3 or greater than 3, so it's not an outlier. - 105 mph: z = (105 - 100) / 15 = 5 / 15 = 0.33, which is not less than -3 or greater than 3, so it's not an outlier. Therefore, 50 mph is the only outlier.

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