A teacher informs her computational physics 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 32 and a standard deviation of 7.8. 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 32.4, but not a 31.67.)

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 72%
and below the top 15%
C Scores above the bottom 28%
and below the top 28%
D Scores above the bottom 15%
and below the top 72%
F Bottom 15%