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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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Chapter
Section
BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

Find each of the requested values for a population with a mean of μ = 50 and a standard deviation of σ = 20.

a. What is the z -score corresponding to X = 52?

b. What is the X value corresponding to z = -0.50?

c. If all of the scores in the population are transformed into z-scores, what will be the values for the mean and standard deviation for the complete set of scores?

d. What is the z-score corresponding to a sample mean of M = 42 for a sample of n = 4 scares?

e. What is the z-score corresponding to a sample mean of M = 42 for a sample of n = 16 scores?

a.

To determine

To find: The value of z when X=52

Explanation

Given info:

Score follows normal distribution with mean 50 and standard deviation 20.

Calculation:

Let μ and σ be the mean and standard deviation of score X respectively. Then,

μ=50σ=20

The formula for finding the z score is,

<

b.

To determine

To find: The value of X when z=0.5

c.

To determine

To find: The value of mean and standard deviation when the values are transformed into z-score.

d.

To determine

To find: The value of z when n=4

e.

To determine

To find: The value of z when n=16

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