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A teacher informs his organic chemistry class (of 500+ students) that a test was very difficult,...

A teacher informs his organic chemistry 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 33 and a standard deviation of 8.7. 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 33.2, but not a 32.73.) The grades are curved according to the following scheme.

Find the numerical limits for each letter grade.

Letter Scheme Interval
A Top 14%
B Scores above the bottom 65% and below the top 14%
C Scores above the bottom 35% and below the top 35%
D Scores above the bottom 14% and below the top 65%
F Bottom 14%

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