The Boeing 757-200 ER airliner carries 200 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 stand deviation of 2.8 in.
A) What doorway height would allow 95% of men to enter the aircraft without bending?
B) Assume half of the 200 passengers are men. What doorway height satisfies the condition that there is a 0.95 probability that this height is greater than the mean height of the 100 men?