Questions: A successful basketball player has a height of 6 feet 7 inches, or 201 cm. Based on statistics from a data set, his height converts to the z score of 3.74. How many standard deviations is his height above the mean? The player's height is standard deviation(s) above the mean. (Round to two decimal places as needed.)

A successful basketball player has a height of 6 feet 7 inches, or 201 cm. Based on statistics from a data set, his height converts to the z score of 3.74. How many standard deviations is his height above the mean?

The player's height is standard deviation(s) above the mean. (Round to two decimal places as needed.)

Transcript text: A successful basketball player has a height of 6 feet 7 inches, or 201 cm . Based on statistics from a data set, his height converts to the $z$ score of 3.74 . How many standard deviations is his height above the mean? The player's height is $\square$ standard deviation(s) above the mean. (Round to two decimal places as needed.)

Solution

Solution Steps

Step 1: Understanding the $z$ score formula

The $z$ score of a data point is calculated using the formula: \[z = \frac{X - \mu}{\sigma}\] where:

$X$ is the value of the data point, in this case, the player's height.
$\mu$ is the mean of the data set, which represents the average height.
$\sigma$ is the standard deviation of the data set, indicating how much variation there is from the average height.

Given that the $z$ score is provided, it represents how many standard deviations the player's height is above or below the mean height.

Step 2: Interpreting the $z$ score

The provided $z$ score, 3.74, directly indicates the number of standard deviations the player's height is above (or below) the mean height. This means that the player's height is 3.74 standard deviations away from the mean height of the population.