A statistics teacher wants to grade test on a curve. She has found that the mean of test was 72% with standard deviation of 6%. If the teacher wants the top 15% of the class to get an A, what would be the cut-off score be? If middle 30% receive a grade of a C, what would the cut-offs be? If the lowest 10% receive an F, what would the cut-off be? Provide a cut-off for each letter grade.
Please show all work.