Normal Distribution test scores

Question

Scores on a certain math test are normally distributed with a mean of 68 and a standard deviation of 15. The instructor decides to set the grade cut-off points such that the top 20% of the students get an A, the NEXT 30% get a B, and the NEXT 40% will get a C. (the rest will get a D or F). What should be the cut-off scores for A,B, and C?

Answer 1

The top 20 percent of students (A grade) must be above a z-score of 0.8416

The top 50 percent (B or better) must be above a z-score of 0.0

The top 90 percent (C or better) must be above a z-score of -1.2816

(These z-score values can be found in a table of standard normal distribution values or by using the INV NORM function on a calculator or spreadsheet.)

So an A grade would be 0.8416 standard deviations above the mean, or 68 + 0.8416(15) = 80.62

A B grade would correspond to a z-score of 0, which is at the mean = 68.0

The C grade cut-off would be 1.2816 standard deviations BELOW the mean (the z-score is negative), or 68 - 1.2816(15) = 48.78