Question

an airliner carries 300 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).
a. if a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.
the probability is.9838.
(round to four decimal places as needed.)
b. if half of the 300 passengers are men, find the probability that the mean height of the 150 men is less than 75 in.
the probability is 1.
(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 flights where the mean height of the male passengers will be less than the door height.
b. the probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.
c. 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.
d. the probability from part (b) 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. 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.
b. since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.
c. there is no adequate reason to ignore women. a separate statistical analysis should be carried out for the case of women.

Explanation:

Step1: Analyze the context

The problem is about comparing the relevance of probabilities from parts (a) and (b) in the context of airline passenger heights. Part (a) is about an individual male passenger, and part (b) is about the mean height of a sample of male passengers.

Step2: Consider the nature of the problem

When considering the comfort and safety of passengers, we are dealing with groups (all passengers on a flight). The probability from part (b) relates to the mean height of a group (150 men in this case). Since we care about the overall situation for a flight (a group of passengers), the probability that relates to the group (mean height) is more relevant.

Step3: Evaluate the options

Option B states that 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. This makes sense as flights are groups of passengers, and the mean height of a sample (which can represent the group on a flight) is crucial for determining if the flight - group of passengers will have issues with the door height.

Answer:

B. 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.