Question

A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 12% of scores B: Scores below the top 12% and above the bottom 58% C: Scores below the top 42% and above the bottom 24% D: Scores below the top 76% and above the bottom 9% F: Bottom 9% of scores.

Scores on the test are normally distributed with a mean of 66.8 and a standard deviation of 9.8. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

Answer 1

Solution:

We are given

Population mean = µ = 66.8

Population standard deviation = σ = 9.8

We have to find minimum score required for an A grade.

We know that top 12% of scores have grade A.

So, we have to find critical value for below 88% area or above 12% area by using z-table.

So, required z critical value = 1.174987

(by using z-table)

Required Minimum score for grade A is given as below:

Required score = µ + Z*σ = 66.8 + 1.174987*9.8 = 78.31487

Minimum score required for Grade A = 78

Answer: 78