A small aircraft carries 20 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 3.5 in.

a) If a male passenger is randomly selected, what is the probability that he can fit through the doorway without bending? __________

b) If half of the passengers are men, find the probability that the mean height of the men is less than 72 in.