Question

A distribution of exam scores has a mean of µ = 42.

a. If your score is X= 46, which standard deviation would give you a better grade: sigma = 5 or sigma = 10?
b. If your score is X = 38, which standard deviation would give you a better grade: sigma = 5 or sigma = 10?

Answer 1

To determine the better grade for given scores, calculate the z-scores for each standard deviation. A higher z-score indicates a better grade.

Step-by-step explanation:

To determine which standard deviation would give you a better grade, we need to calculate the z-score for each score. The formula to calculate the z-score is (X - µ) / σ, where X is the score, µ is the mean, and σ is the standard deviation.

a. For X = 46, z-score with - σ = 5 is (46 - 42) / 5 = 4 / 5 = 0.8. For σ = 10, z-score is (46 - 42) / 10 = 4 / 10 = 0.4. Since a higher z-score indicates a better grade, the standard deviation of 5 would give you a better grade.

b. For X = 38, z-score with σ = 5 is (38 - 42) / 5 = -4 / 5 = -0.8. For σ = 10, z-score is (38 - 42) / 10 = -4 / 10 = -0.4. Again, since a higher z-score indicates a better grade, the standard deviation of 10 would give you a better grade.