Suppose a new student honors society, Alpha Alpha Alpha, is going to start at Harvard. Alpha Alpha Alpha aims to be exclusive and only wants the best students.Currently, there are about 10,000 students enrolled at Harvard. We also know that the average GPA of Harvard students is normally distributed with a mean of 3.3 with a standard deviation of .15.
(A) If Alpha Alpha Alpha requires a 3.9 GPA, how many students will be eligible for membership?
(B) Alternatively, suppose Alpha Alpha Alpha decides it wants the top 2% of students at Harvard, what should it set its GPA requirements at?
(C) If we did not know that the grade distribution at Harvard was normal, is there any other technique we can apply to find out the number of students between two intervals?