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.

Answer 2

The standard deviation should be 5.17.

Calculation of standard deviation:

We know that the z score represents the number of standard deviations that should be above the mean, a particular value is.

Here Normal distribution means the probability distribution that should be symmetrically related to the mean, also it represents that data that is near the mean.

So, in the given situation, the height should be converted to the z-score of 5.17 so this represents that his height is 5.17 i.e. standard deviations above mean

Learn more about the mean here: https://brainly.com/question/1863752