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Essentials of Statistics for the B...

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

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BuyFindarrow_forward

Essentials of Statistics for the B...

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

A distribution with a mean of μ = 38 and a standard deviation of σ = 5 is transformed into a standardized distribution with μ = 50 and σ = 10. Find the new, standardized score for each of the following values from the original population.

a.    X = 39

b.    X = 43

c.    X = 35

d.    X = 28

a.

To determine

To find: The new standardized score for X=39 from the original population.

Explanation

Given Info:

The population has a mean of μ=38 and a standard deviation σ=5, score of X=39.

The new distribution has a mean of μ=50 and a standard deviation σ=10.

Calculation:

Use the formula of z score to transform the original raw scores into z-scores as follows:

z=Xμσ

The formula of specified value of X is,

X=μ+zσ

Substitute the value 39 for X, 38 for μ and 5 for σ

b.

To determine

To find: The new standardized score for X=43 from the original population.

c.

To determine

To find: The new standardized score for X=35 from the original population.

d.

To determine

To find: The new standardized score for X=28 from the original population.

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