My teacher makes us read the book to learn and the book doesnt show how to solve something like this

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.