Question

A Math Teacher looked at the NORMALLY distributed results of a recent quiz.

The mean was 71%, and the standard deviation was 8.
He then decided to curve the grades based on Z-scores.
If a Z-score of 1.6 gets an A, what grade on the quiz was that?
Enter you response with 1 decimal place.

Answer 1

83.8

Explanation:

use the z-score formula:

z = (X - μ) / σ

where X is the test statistic (the grade we're trying to find in this case), μ is the mean, σ is the standard deviation.

z = (X - μ) / σ

1.6 = (X - 71) / 8

8(1.6) = X - 71

12.8 = X - 71

X = 12.8 + 71

= 83.8.

z-score of 1.6 (A grade) is grade of 83.8