Question: A set of final examination marks in an introductory statistics unit is normally distributed with a mean of 73 and a standard deviation of 8.

a) What is the probability of getting a mark of 91 or less?

b) What is the probability that a student obtains a mark between 65 and 89?

c) If the lecturer gives Distinction and High Distinction grades to the top 15% of students, what mark does a student need to get a distinction?

d) If the lecturer gives grades of High Distinction to the top 5% of students, are you better off with a mark of 80 on this exam or a mark of 68 on a different exam where the mean is 62 and the standard deviation is 3? Show your answer statistically and explain.