A teacher informs his advanced music theory 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 42 and...

A teacher informs his advanced music theory 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 42 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 42.5, but not a 41.83.)


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

Letter	Scheme	Interval
A	Top 15%
B	Scores above the bottom 74% and below the top 15%
C	Scores above the bottom 26% and below the top 26%
D	Scores above the bottom 15% and below the top 74%
F	Bottom 15%