Question

z Scores LeBron James, one of the most successful basketball players of all time, has a height of 6 feet 8 inches, or 203 cm. Based on statistics from Data Set 1 “Body Data” in Appendix B, his height converts to the z score of 4.07. How many standard deviations is his height above the mean?

Short answer

The given height equal to 203 cm is 4.07 standard deviations above the mean height.

Step-by-step solution

Given information

The given data shows the heights of a population of 300 males and females measured in cm.

Z-score

Thez-scoreprovides an idea of how many standard deviations a data value is above or below the mean value. For a given sample, it has the following expression:

$Z=\frac{x-\overline{x}}{s}$

Here,

x is any data value.

$\overline{x}$ is the sample mean.

s is the sample standard deviation.

For example, a sample consists of time durations taken by a group of employees to complete a given task. The average time is equal to 14 minutes, and the standard deviation is equal to 5.4 minutes.

The z-score of a time duration equal to 7 minutes is equal to -1.29. Thus, it can be said that the time duration equal to 7 minutes is 1.29 standard deviations below the mean value.

Interpretation of z-score

The z-score value for a given value of height equal to 203 cm is obtained as 4.07.

This implies that the value of the height is4.07 standard deviations above the mean.