Entry to a certain university is determined by a national exam. The scores on this exam are normally distributed with a mean of 72 and a standard deviation of 6. Suppose, 5400 students undertake the university entrance exam, apply the properties of the normal distribution to answer the following questions:

a)How many students are expected to score between 66 and 72?

b)How many students are expected to score between 60 and 84?

c)How many students will be admitted to the university if the entry cut-off mark was 66?

d)What is the lowest student mark amongst the highest 2.5% of students?

e)What is the highest student mark amongst the lowest 2.5% of students?