Question

an airliner carries 400 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 2.8 in. complete parts (a) through (d).
c. the probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.
d. the probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.
d. when considering the comfort and safety of passengers, why are women ignored in this case?
a. there is no adequate reason to ignore women. a separate statistical analysis should be carried out for the case of women.
b. since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. therefore, it is more important that men not have to bend than it is important that women not have to bend.
c. since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

Explanation:

When considering door height for passenger comfort and safety, men are often the focus in such problems. This is because men, on average, have a greater height compared to women. If a door height is designed to accommodate a significant proportion of men (who are taller), it will inherently accommodate an even larger proportion of women (who are shorter on average). So, a design that works for men in terms of height - related comfort (not having to bend) will also work well for women.

Answer:

C. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.