Question

A college commerce society has provided printed logo promotional t-shirts to all commerce

students. In order to cater for different sizes, the society assumes the heights of students

follow a normal distribution with a mean of 170cm and a standard deviation of 6.5cm.

(i) What is the probability that a randomly selected student will have a height less than

180 cm?

(ii) A medium sized t-shirt is stated to fit a student with height in the range 160cm to

180cm. What proportion of the population would require a medium sized t-shirt?

(iii) An XL sized t-shirt is needed for the tallest 2.5% of the population of commerce

students. Above what height should be categorised as XL? i.e. If 2.5% of the

population of commerce students have heights greater than K cm, find the value of K.

Answer 1