Suppose that the height of Australian males is a normallydistributed random variable with a mean of 176.8cm and a standarddeviation of 9.5cm.

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

b. Calculate (using the appropriate statisticaltables) the probability that a randomly selected Australian man ismore than two metres tall.

c. To become a jockey, as well as a passion forthe sport, you need to be relatively small, generally between 147cmand 168cm tall. Calculate (using the appropriate statisticaltables) the proportion of Australian males who fit this heightrange.

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

e. Verify your answers to parts b., c. and d.using the appropriate Excel statistical function and demonstrateyou have done this by including the Excel formula used.

f. A random sample of forty Australian males isselected. State the type of distribution and the value/s of theparameter/s for the mean of this sample.

g. Calculate (using the appropriate statisticaltables) the probability that the average height of this sample isless than 170cm.