A teacher finds that the scores of a particularly difficult test were approximately normally distributed with a mean of 76 and standard deviation of 14.

(a) If a score below 60 represents a grade of F (failure), approximately what percent of students failed the test?

(b) If the cutoff for a grade of A is the lowest score of the top 10%, what is that cutoff point?

(c) How many points must be added to the students’ scores so that only 5% fail?