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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

A distribution with a mean of μ = 76 and a standard deviation of σ = 12 is transformed into a standardized distribution with μ = 100 and σ = 20. Find the new, standardized score for each of the following values from the original population.

a.    X = 61

b. X = 70

c.    X = 85

d. X = 94

(a)

To determine

To find: The new standardized score for X=61 from the original population.

Explanation

Given info:

The sample has a mean of M=76 and a standard deviation s=12 score of X=61. The new distribution has a mean of μ=100 and a standard deviation σ=20

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,

(b)

To determine

To find: The new standardized score for X=70 from the original population.

(c)

To determine

To find: The new standardized score for X=85 from the original population.

(d)

To determine

To find: The new standardized score for X=94 from the original population.

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