A teacher informs his macro economics class (of 500+ students) that a test was v

Question

A teacher informs his macro economics class (of 500+ students) that a test was very difficult, but the grades would be curved. Scores on the test were normally distributed with a mean of 34 and a standard deviation of 7.9. The maximum possible score on the test was 100 points. Because of partial credit, scores were recorded with 1 decimal point accuracy. (Thus, a student could earn a 34.1, but not a 33.06.)

The grades are curved according to the following scheme. Find the numerical limits for each letter grade.

Letter Scheme Interval A Top 8% B Scores above the bottom 70%
and below the top 8% C Scores above the bottom 30%
and below the top 30% D Scores above the bottom 8%
and below the top 70% F Bottom 8%

Explanation / Answer

The normal distribution probabilities are calculated using the below link:

https://planetcalc.com/4987/

Letter Scheme Interval A Top 8% 45.1 to 100 B Below top 8% and above bottom 70% 38.1 to 45 C Above bottom 30% and below top 30% 29.8 to 38 D Above bottom 8% and below top 70% 23 to 29.7 F Bottom 8% 0 to 22.9

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