Question

A successful basketball player has a height of 6 feet 11 ​inches, or 211 cm. Based on statistics from a data​ set, his height converts to the z score of 5.17. How many standard deviations is his height above the​ mean?

Answer 1

Answer:

$z=\frac{x-\mu}{\sigma}$

And we know that the value for z= 5.17

And that means that the height is 5.17 deviations above the population mean,

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(\mu,\sigma)$  

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

And we know that the value for z= 5.17

And that means that the height is 5.17 deviations above the population mean.