Please show work

2. The Boeing 757-200 ER airliner carries 200 passengers and has doors with a height of 72 in. Heights of women are normally distributed with a mean of 64.5 inches with a standard deviation of 2.5 inches. a. If a women passenger is randomly selected, find the probability that she can fit through the doorway without bending. b. If half of the 200 passengers are women, find the probability that the mean height of the 100 women is less than 72in. c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b) and why