Chapter 2.1, Problem 15E

(a)

To determine

Interpretation of the z − score.

Explanation of Solution

Given information:

z − score,

  $z=1.10$

The z − score describes the number of standard deviations that a value is from the mean.

Negative z − score indicates that the value is below the mean.

Whereas,

Positive z − score indicates that the value is above the mean.

Thus,

According to the sample, 22 pairs of shoes that Jackson owns is 1.10 standard deviations above the mean number of the pairs of shoes owned by the other students.

(b)

To determine

Mean of the distribution using the information along with Jackson’s z − score.

Answer to Problem 15E

Mean of the distribution,

  $\mu =11.638$

Explanation of Solution

Given information:

Value, $x=22$

Standard deviation, $\sigma =9.42$

z − score, $z=1.10$

Calculations:

Calculate the z − score:

  $z=\frac{x-\mu }{\sigma }$

Substitute values,

  $1.10=\frac{22-\mu }{9.42}$

Multiply both sides by 9.42:

  $10.362=22-\mu$

That becomes

  $\mu =22-10.362=11.638$

Since the units of the mean and the data values are same.

Thus,

The mean is 11.638 pairs of shoes.