Question

A successful basketball player has a height of 6 feet 3 inches, or 191 cm. Based on statistics from a data set, his height converts to the z score of 2.31. How many standard deviations is this player's height above or below the mean?

Answer 1

The player's height is approximately 0.97 standard deviations below the mean.

Step-by-step explanation:

To determine how many standard deviations a player's height is above or below the mean, we use the formula:

z = (x - μ) / σ

Where:

• z is the z-score
• x is the player's height
• μ is the mean height
• σ is the standard deviation

In this case, the player's height is 191 cm with a z-score of 2.31. The mean height is 79 inches (200.66 cm) and the standard deviation is 3.89 inches (9.88 cm).
Using the formula, we can calculate:

z = (191 - 200.66) / 9.88 = -0.97

The player's height is approximately 0.97 standard deviations below the mean.