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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 distribution of exam scores has a mean of μ = 78.

  1. a. If your score is X = 70, which standard deviation would give you a better grade: σ = 4 or σ = 8?
  2. b. If your score is X = 80, which standard deviation would give you a better grade: σ = 4 or σ = 8?

a.

To determine

To identify: Which standard deviation would give you a better grade σ=4 or σ=8 if score is X=70.

Explanation

Given info:

The data represents the mean, standard deviation and x-score of the distribution. The exam score mean is μ=78 and the score is X=70.

Calculation:

The general formula for z score is,

z=Xμσ

Case 1:

z-score corresponding to X=70 with standard deviation σ=4:

Substitute the value 70 for X, 78 for μ and 4 for σ.

z=Xμσ=78704=84=2

Thus, the value of z-score is 2.

Case 2:

z-score corresponding to X=70

b.

To determine

To identify: Which standard deviation would give you a better grade σ=4 or σ=8 if score is X=80.

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