Question

A psychology professor assigns letter grades on a test according to the following scheme. A: Top 13% of scores B: Scores below the top 13% and above the bottom 57% C: Scores below the top 43% and above the bottom 22% D: Scores below the top 78% and above the bottom 8% F: Bottom 8% of scores Scores on the test are normally distributed with a mean of 71 and a standard deviation of 8.1. Find the numerical limits for a C grade. Round your answers to the nearest whole number, if necessary.

Answer 1

Given information:

The C grade is above the bottom 0.22 and below the top 0.43. Here we need z-score that has 0.22 area to its left. The z-score -0.772 has 0.22 area to its left using excel function "=NORMSINV(0.22)". The lower limit of C grade is

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Here we need z-score that has 0.57 area to its left. The z-score 0.176 has 0.57 area to its left (that is 0.43 area to its right) using excel function "=NORMSINV(0.57)". The lower limit of C grade is

The required numerical limits are (65, 72).