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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 of English exam scores has μ = 50 and σ = 12. A distribution of history exam scores has μ = 58 and σ = 4. For which exam would a score of X = 62 have a higher standing? Explain your answer.

To determine

To explain: The exam for which the score X=62 would have a higher standing.

Explanation

Given Info:

The English exam score has a mean of μ=50 and a standard deviation of σ=12.

The distribution of history exam has a mean of μ=58 and a standard deviation σ=4.

The X-score is 62.

Calculation:

The z-score is used to transform any distribution in to standardized distribution with a predetermined mean and a predetermined standard deviation.

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

z=Xμσ

For English Exam:

Substitute the value 62 for X, 50 for μ and 12 for σ.

z=Xμσ=625012=1

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