Question

an airliner caries 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).
the probability is 1.0000.
(round to four decimal places as needed.)
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)? why?
○ a. the probability from part (b) 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.
○ b. the probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend.
○ 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.

Explanation:

When considering passenger comfort and safety, the mean height of passengers on a flight (which is what part (b)’s probability relates to, as it’s about the sample mean) is crucial. Part (a) is about an individual, but for an airliner, the group (sample mean) is more relevant. The probability from part (b) shows the proportion of flights where the mean height of male passengers will be less than the door height.

Answer:

A. The probability from part (b) 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.