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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 population with a mean of μ = 44 and a standard deviation of σ = 6 is standardized to create a new distribution with μ = 50 and σ =10.

  1. a. What is the new standardized value for a score of X = 47 from the original distribution?
  2. b. One individual has a new standardized score of X = 65. What was this person’s score in the original distribution?

(a)

To determine

To Find: The new standardized score for X=47 from the original distribution.

Explanation

Given Info:

The population has a mean of μ=44 and a standard deviation σ=6, score of X=47.

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

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

The formula of specified value of X is,

X=μ+zσ

Substitute the value 47 for X, 44 for μ and 6 for σ

(b)

To determine

To find: The person’s score in the original distribution.

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