Question

an airliner carries 200 passengers and has doors with a height of 75 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 (a) is more relevant because it shows the proportion of male passengers that will not need to bend.
b. 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.
c. the probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend.
d. 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.

Explanation:

When considering passenger comfort and safety, the proportion of individual male passengers who do not need to bend (which relates to the probability of an individual's height being less than the door height) is crucial. Part (a) would likely be about the probability for an individual (since part (b) might be about the sample mean, e.g., using the Central Limit Theorem for the mean of a sample). For comfort and safety of each passenger, the individual - level probability (from part (a)) is more relevant as it pertains to each person's experience (not the mean of a group of passengers in a flight).

Answer:

A. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.