If the mean score is 55% and the s.d. is 15%, then a test score of at least
55% + 1.5 × 15% = 77.5%
falls in the A range.
The next cutoff score is 0.5 s.d. from the mean, which is
55% + 0.5 × 15% = 62.5%
so any test score between 62.5% and 77.5% is in the B range.
The next cutoff is
55% - 0.5 × 15% = 47.5%
so a score between 47.5% and 62.5% gets a C.
The lower limit of the next range is
55% - 1.5 × 15% = 32.5%
so 32.5% - 47.5% gets a D.
Anything lower than 32.5% is an F.