Question

Solve the problem. A history teacher assigns letter grades on a test according to the following scheme: A: Top 10% B: Scores below the top 10% and above the bottom 60% C: Scores below the top 40% and above the bottom 20% D: Scores below the top 80% and above the bottom 10% F: Bottom 10% Scores on the test are normally distributed with a mean of 68 and a standard deviation of 12.5. Find the numerical limits for each letter grade.

Answer 1

Given that

Let X is a random variable shows the score.

For grade A:

The z-score 1.28 has 0.10 area to its right and 0.90 area to its left so score corresponding to grade A is

That is scores greater than equal to 84 will receive letter A.

For grade B:

Using excel function "=NORMSINV(0.6)", the z-score 0.25 has 0.60 area to its left so lower score corresponding to grade B is

That is scores greater than 71 and less than 84 will receive letter B.

For grade C:

Using excel function "=NORMSINV(0.2)", the z-score -0.84 has 0.20 area to its left so lower score corresponding to grade C is

That is scores greater than equal to 57.5 and less than equal to 71 will receive letter C.

For grade D:

Using excel function "=NORMSINV(0.10)", the z-score -1.28 has 0.10 area to its left so lower score corresponding to grade D is

That is scores greater than equal to 52 and less than 57.5 will receive letter D.

For grade F:

Using excel function "=NORMSINV(0.10)", the z-score -1.28 has 0.10 area to its left so upper score corresponding to grade F is

That is scores less than 52 will receive letter F.