3) (20 pts.) (Section 6.4 in book) A professor determined that the grades on a stats test are normally distributed with mean grade of 68 and standard deviation of 15.

a) If Anna scored a 75 what z-score does this correspond to?

b) If Mohammed's grade corresponds to a z-score of 1.25, what is his grade?

c) The top 12% of scorers will receive the letter grade A. What is the lowest grade a student can get and still get an A? Please draw and label the appropriate diagram that helps solve this problem.

d) The bottom 15% of scorers will receive an F. What is the highest grade that results is an F? Draw a diagram as for part c)