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 10 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: 65 ​mph, 110 ​mph, and 120 mph.

Answer 1

The speed of 65 ​mph is an outlier in the distribution of the​ player's serve​ speeds

Explanation:

We are given the following information in the question:

Mean, μ = 100 mph

Standard Deviation, σ = 10 mph

Formula:

`z_(score) = \displaystyle(x-\mu)/(\sigma)`

Outlier on basis of z-score:

• Any z-score greater than 3 or less than -3 is considered to be an outlier.
• This rule of thumb is based on the empirical rule.

Calculation of z-score:

`x = 65\Rightarrow z = (65-100)/(10) = -3.5\\\\x = 110\Rightarrow z = (110-100)/(10) = 1\\\\x = 120\Rightarrow z = (120-100)/(10) = 2`

Thus, the speed of 65 ​mph is an outlier in the distribution of the​ player's serve​ speeds as the corresponding z-score is less than -3.