Question

a successful basketball player has a height of 6 feet 8 inches, or 203 cm. based on statistics from a data set, his height converts to the z score of 4.10. how many standard deviations is his height above the mean?
the players height is □ standard deviation(s) above the mean.
(round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x\) is the data point, \(\mu\) is the mean, and \(\sigma\) is the standard deviation. The z - score represents the number of standard deviations a data point is from the mean.

Step2: Interpret the z - score value

Given that the z - score \(z = 4.10\). By the definition of the z - score (\(z=\frac{x-\mu}{\sigma}\)), when \(z>0\), the data point \(x\) (in this case, the player's height) is above the mean. The value of \(z\) itself gives the number of standard deviations.

Answer:

\(4.10\)