An airline carriers 300 passengers and has doors with a height of 76 inch. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in.
a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
b. If half of the 100 passengers are men, find the probability that the mean height of the 50 men is less than 78 in.
c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from (b)
d. When considering the comfort and safety of passengers, why are women ignored in this case?