Question

A distribution of scores has a mean of LaTeX: \muμ= 80. If your score is X = 72, which standard deviation would give you a better grade: LaTeX: \sigmaσ= 4 or LaTeX: \sigmaσ= 6? If your score is X = 90, which standard deviation would give you a better grade: LaTeX: \sigmaσ= 5 or LaTeX: \sigmaσ= 10?

Answer 1

A standard deviation of scores has a mean of 80. The score is X=72.

Now, if sigma is 4, then the grade is the z-score is

=(72-80)/4

=-8/4

=-2

Now, if sigma=6, then the grade is the z-score is

=(72-80)/6

=-8/6

=-1.33

So, as the z-score -1.33 is more than the z-score -2, then the sigma=6 will give a better score for X=72.

Now, if the score is X=90.

Then, sigma=5 will give a grade or z-score of

=(90-80)/5

=2

And, the z-score of sigma=10 is

=(90-80)/10

=1

So, as the z-score of 2 is more than the z-score of 1, so sigma=5 will give a better grade.