An airline carries 400 passengers and has doors with a height of 78in. Heights of men are normally distributed with a mean of 69.0in and a standard deviation of 2.8in.

a.) If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. Round to four decimal places.

b.) If half of the 400 passengers are men, find the probabilityy that the mean height of the 200 men is less than 78in. Round to four decimal places.

c.) When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or probability from part (b).

d.) When considering the comfort and safety of passengers, why are women ignored in this case?