Question

An English professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 59% C: Scores below the top 41% and above the bottom 17% D: Scores below the top 83% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 79.7 and a standard deviation of 9.7. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answer 1

67 and 70

Explanation:

Mean grade (μ) = 79.7

Standard deviation (σ) = 9.7

D: Scores below the top 83% and above the bottom 9%, which means scores between the 9th and 17th percentile.

z-score at the 9th percentile: -1.34

z-score at the 17th percentile: -0.955

The lower limit of a D grade is:

`-1.34=(L-\mu)/(\sigma)\\-1.34=(L-79.7)/(9.7)\\ L=66.7`

The upper limit of a D grade is:

`-0.955=(U-\mu)/(\sigma)\\-0.955=(U-79.7)/(9.7)\\ L=70.4`

Rounding to the nearest whole number, the limits for a D grade are 67 and 70.