Scores for an entry exam to a university are normally distributed with a mean of 75 and a standard deviation of 6.5:

a) If the top 5% are admitted with a full scholarship, what is the lowest score a student can obtain to earn a full scholarship?

b) The university decides that students who scores below or at the 10th percentile must take remedial courses. If a student scores 63 on the entry exam, will he/she be taking remedial courses? Explain why.

c) What is the probability that a randomly selected student will score more than 90?