Assume that the height of South African adult males has the normal distribution, with an average of 166 cm and a standard deviation of 9 cm. Let X be the sample mean of the heights of a sample of 20 men.

(a) Describe the distribution of X; giving the name of the distribution, its expected value and variance. (5)

(b) What is the probability that the sample mean is between 156 cm and 176 cm? (7)

(c) Find the first and third quartiles of the distribution of the sample mean. (8)