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Chapter 2: Q90E (page 116)

Compute the z-score corresponding to each of the following values of x:

a. x = 40, s = 5, X= 30

b. x = 90, μ= 89, σ= 2

c. μ= 50, σ= 5, x = 50

d. s = 4, x = 20, X= 30

e. In parts a–d, state whether the z-score locates x within a sample or a population.

f. In parts a–d, state whether each value of x lies above or below the mean and by how many standard deviations.

Short Answer

Expert verified

  1. The z-score of 40 is 2.

  2. The z-score of 89 is 0.2.

  3. The z-score of 50 is0.

  4. The z-score of 20 is (-2.5.)

  5. A and d lie in the sample, whereas b and c are from a population.

  6. According to the z-score values, a–c lie above the mean and d lies below the mean.

Step by step solution

01

Computing the z-score for aa.

z=x-xs=40-305=105=2

As the z-score of 40 is 2, it is not an outlier.

02

Finding the z-score for bb.

z=x-μσ=90-892=15=0.2

The z-score of 90 is 0.2.Hence, it is not an outlier.

03

Finding the z-score for cc.

z=x-μσ=50-505=05=0

As the z-score is0, 50 is not an outlier.

04

Finding the z-score for dd.

z=x-xs=20-304=-104=-2.5

Thus, z=(-2.5), and 20 is not an outlier.

05

Determining whether the values of x are from a sample or a populatione.

  1. x = 40 is from a sample.

  2. x = 90 is from a population.

  3. x = 50 is from a population.

  4. x = 20 is from a sample.

06

Identifying the location of x with respect to the meanf.

We can summarize with the following:

  1. The value of x = 50 lies 2 standard deviations above the mean.

  2. x = 90 lies 0.2 standard deviation above the mean.

  3. x = 50 = μ.

  4. x = 20 lies 2.5 standard deviations below the mean.

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Most popular questions from this chapter

Defects in new automobiles.Consider the following data from the automobile industry. All cars produced on a particular day were inspected for defects. The 145 defects found were categorized by type as shown in the accompanying table.

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State

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1

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Florida

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3

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2

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5

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4

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2

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