Question

A humanities 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 63% C: Scores below the top 37% and above the bottom 15% D: Scores below the top 85% and above the bottom 9% F: Bottom 9% of scores Scores on the test are normally distributed with a mean of 68 and a standard deviation of 7.6. Find the minimum score required for an A grade. Round your answer to the nearest whole number, if necessary.

Answer 1

Let 'a' denote the minimum score required for an A grade; and

X denote the random variable representing the scores of students in the test.

Now,

Now, since only top 12% of scores get an A grade and the minimum score for getting an A grade is 'a'. Thus, we get:

Now, from the table of standard normal distribution, we get :

P(Z > 1.17499) = 0.12

Thus,

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