5.The final total score (assignments + participation + exams + final project) on a Math course has mean of 90 and variance of 5. Assuming the final score X is normally distributed and given the grading scheme is as follows:

B:80 < X 83;B:83< X 87;B+:87 < X 90;

A:90 < X 94;A:94 < X 100;

a. What percentage of the students get an A, and A-, and a B+?

b.How high need a score X be on this exam so that only 1% of the students score higher than X. What is this score called?

c. The final scores for another section of the course is also normally distributed with mean 90, but the variance is smaller than 5. How do the 95% percentiles compare between the two sections? Why?