Suppose that the height of Australian males is a normally distributed random variable with a mean of 176.8cm and a standard deviation of 9.5cm.

a. If the random variable X is the height of an Australian male, identify the distribution of X and state the value/s of its parameter/s.

b. Calculate (using the appropriate statistical tables) the probability that a randomly selected Australian man is more than two metres tall.

c. To become a jockey, as well as a passion for the sport, you need to be relatively small, generally between 147cm and 168cm tall. Calculate (using the appropriate statistical tables) the proportion of Australian males who fit this height range.

d. Some of the smaller regional planes have small cabins, consequently the ceilings can be quite low. Calculate (using the appropriate statistical tables) the ceiling height of a plane such that at most 2% of the Australian men walking down the aisle will have to duck their heads.

e. A random sample of forty Australian males is selected. State the type of distribution and the value/s of the parameter/s for the mean of this sample.

f. Calculate (using the appropriate statistical tables) the probability that the average height of this sample is less than 170cm.