Question

A philosophy professor assigns letter grades on a test according to the following scheme.

A: Top 10%of scores

B: Scores below the top 10%and above the bottom 58%

C: Scores below the top 42%and above the bottom 20%

D: Scores below the top 80%and above the bottom 9%

F: Bottom 9%of scores

Scores on the test are normally distributed with a mean of 67.3and a standard deviation of 7.3. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.

Answer 1

Given = 67.3, 7.3

To find the probability, we need to find the z scores.

The Limits for grade D lie above 9% and below 20%

The Lower Limit: P(X < x) = 0.09

The z score for a p value of 0.09 is = -1.3408

Therefore (X - 67.3) / 7.3 = -1.3408

Solving for X, X = (-1.3408 * 7.3) + 67.3 = 51.51    52 (Rounding to the nearest whole number)

The Upper Limit: P(X < x) = 0.2

The z score for a p value of 0.2 is = -0.8416

Therefore (X - 67.3) / 7.3 = -0.8416

Solving for X, X = (-0.8416 * 7.3) + 67.3 = 61.15    61 (Rounding to the nearest whole number)

Therefore the numerical limits for D are scores from 52 to 61