Question

Determine the whole number of standard deviations that includes all data values. The mean price of the nonfiction books on a best-sellers list is $ 22.58 ; the standard deviation is $ 3.00 .
$ 22.95, $ 18.00, $ 21.00, $ 21.00, $ 22.00, $ 25.00, $ 29.95, $ 22.00, $ 22.95, $ 20.95
All of the values fall within____standard deviation(s) of the mean.

Answer 1

Using z-scores, it is found that all of the values fall within 2.46 standard deviations of the mean.

What is the z-score formula?

The z-score of a measure X of a variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

The z-score measures how many standard deviations the measure is above or below the mean.

In this problem, the farthest variable from the mean is of $29.95, hence X = 29.95 and:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{29.95 - 22.58}{3}$

Z = 2.46.

Hence, all of the values fall within 2.46 standard deviations of the mean.

More can be learned about z-scores at brainly.com/question/24663213