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Chapter 2: Q93. (page 116)

Compare the z-scores to decide which of the following x values lie the greatest distance above the mean and the greatest distance below the mean.

a.鈥�x=100,鈥�鈥�渭=50,鈥�鈥�蟽=25b.鈥�x=1,鈥�鈥�渭=4,鈥�鈥�蟽=1c.鈥�x=0,鈥�鈥�渭=200,鈥�鈥�蟽=100d.x=10,鈥�鈥�渭=5,鈥�鈥�蟽=3

Short Answer

Expert verified

a.Z=2

b.Z=-3

c.Z=-2

d.Z=1.67

The x values lie the most significant distance above the mean in part (a), and they lie the most significant distance below the mean in part (c).

Step by step solution

01

Computing the z-score when x=100,  μ=50,  σ=25

Z-score can be computed using the formula:Z=x-渭蟽

Substituting the values:

Z=100-5025Z=5025Z=2

Thus, the z-score is 2.

02

Calculating the z-score when x=1,  μ=4,  σ=1

Using the values in the z-score formula, one gets:

Z=1-41Z=-31Z=-3

Therefore, the z-score is -3.

03

Finding the z-score when x=0,  μ=200,  σ=100

Z=0-200100Z=-200100Z=-2

Hence, the z-score is -2.

04

Determining the z-score when x=10,  μ=5,  σ=3

Z=10-53Z=53Z=1.67

Here, the z-score is 1.67

05

Comparing the z-scores

From the z-scores computed above, the x values that lie the greatest distance above the mean isx=100 (part a), and the x values that lie the greatest distance below the mean isx=0 (part c).

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