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Chapter 2: Q 16. (page 106)

Don’t call me Refer to Exercise 4 Alejandro, who sent 92 texts, has a standardized score of z=1.89

a. Interpret this z-score.

b. The standard deviation of the distribution of the number of text messages sent over the past 24 hours by the students in Mr. Williams’s class is 34.15 Use this information along with Alejandro’s z-score to find the mean of the distribution.

Short Answer

Expert verified

Part (a) Alejandro's 92 texts are 1.89 standard deviations over the mean number of texts sent by the students.

Part (b) Mean of the distribution, μ=27.45

Step by step solution

01

Part (a) Step 1: Given information

Value,x=92

Standard deviation, σ=34.15

z−score,z=1.89

02

Part (a) Step 2: Concept

The formula used: z=(x-μ)σ

03

Part (a) Step 3: Explanation

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

The value is below the mean when the z−score is negative.

Whereas,

Positive z−implies that the value is greater than the mean.

Thus,

According to the sample, 92 texts sent by Alejandro are 1.89 standard deviations above the mean number of texts sent by the students.

04

Part (b) Step 1: Calculation

Calculate the z− score:

z=x−μσ

Substitute values,

1.89=92−μ34.15

Multiply both sides by 34.15:

64.55=92−μ

That becomes

μ=92−64.55=27.45

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

Thus,

The mean is 27.45 text messages.

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