An airliner carries 400 passengers and has doors with a height of 78 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d). . . . a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is 0.9993 . (Round to four decimal places as needed.) b. If half of the 400 passengers are men, find the probability that the mean height of the 200 men is less than 78 in. The probability is (Round to four decimal places as needed.)