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Essentials of Statistics for the B...

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

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Section
BuyFindarrow_forward

Essentials of Statistics for the B...

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

A population of scores has μ = 73 and σ = 8. If the distribution is standardized to create a new distribution with μ = 100 and σ = 20, what are the new values for each of the following scores from the original distribution?

a. X = 65    b. X = 71    c. X = 81    d. X = 83

(a)

To determine

To find: The new values for X=65 from the original population.

Explanation

Given Info:

The population has a mean of μ=73 and a standard deviation σ=8, score of X=65.

The new distribution has a mean of μ=100 and a standard deviation σ=20.

Calculation:

The z-score is used to transform any distribution in to a standardized distribution with a predetermined mean and a predetermined standard deviation. The advantage of the X scores transformed to z-score tells that the entire population of scores is transformed into z-scores

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

z=Xμσ (1)

The formula of specified value of X is,

X=μ+zσ (2)

Substitute the value 65 for X, 73 for μ and 8 for σ

(b)

To determine

To find: The new values for X=71 from the original population.

(c)

To determine

To find: The new values for score X=81 from the original population.

(d)

To determine

To find: The new values for score X=83 from the original population.

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