A statistics teacher believes that the final exam grades for her elementary statistics class have a normal distribution with a mean of 82 and a standard deviation of 8.

a. Find the score which separates the top 10% of the scores from the lowest 90% of the scores.

b. The teacher plans to give all students who score in the top 10% of scores an A. will a student who scored a 90 on the exam receive an A? Explain.

c. Find the score which separates the lowest 20% of the scores from the highest 80% of the scores.

d. The teacher plans to give all students who scores in the lowers 10% of scores an F. will a student who scored 65 on the exam receive F? Explain.