An English professor assigns letter grades on a test according to the following scheme. A: Top 14% of scores B: Scores below the top 14% and above the bottom 56% C: Scores below the top 44% and above the bottom 16% D: Scores below the top 84% and above the bottom 10% F: Bottom 10% of scores Scores on the test are normally distributed with a mean of 71.9 and a standard deviation of 7.8. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Grades between 62 and 64 result in a D grade.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

Find the numerical limits for a D grade.

D: Scores below the top 84% and above the bottom 10%

So below the 100-84 = 16th percentile and above the 10th percentile.

16th percentile:

This is the value of X when Z has a pvalue of 0.16. So X when Z = -0.995.

10th percentile:

This is the value of X when Z has a pvalue of 0.1. So X when Z = -1.28.

Grades between 62 and 64 result in a D grade.

3201

step-by-step explanation: