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Chapter 2: Q 15. (page 106)

Shoes Refer to Exercise 1. Jackson, who reported owning 22 pairs of shoes, has a standardized score of z=1.10.

a. Interpret this z-score.

b. The standard deviation of the distribution of the number of pairs of shoes owned in this sample of 20 boys is 9.42. Use this information along with Jackson’s z-score to find the mean of the distribution.

Short Answer

Expert verified

Part (a) Jackson owns 22pairs of shoes, which is 1.10standard deviations more than the mean number of pairs owned by the other students.

Part (b) Mean of the distribution,μ=11.638

Step by step solution

01

Part (a) Step 1: Given information

Value,x=22

Standard deviation, σ=9.42

z− score,z=1.10

02

Part (a) Step 2: Concept

The formula used:z=(value-mean)(standarddeviation)

03

Part (a) Step 3: Explanation

The amount of standard deviations a value deviates from the mean is described by the z-score.

A value below the mean is indicated by a negative z-score.

Whereas,

The value above the mean is indicated by a positive z-score.

Thus,

Jackson owns 22 pairs of shoes, which is 1.10standard deviations more than the mean number of pairs owned by the other students, according to the sample.

04

Part (b) Step 1: Calculation

Calculate the z − score:

z=x−μσ

Substitute values,

1.10=22−μ9.42

Multiply both sides by 9.42:

10.362=22−μ

That becomes

μ=22−10.362=11.638

Because the data values and the mean units are the same.

Thus,

The mean is 11.638 pairs of shoes.

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