Question

an airliner carries 150 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 0.9830
(round to four decimal places as needed.)
b. if half of the 150 passengers are men, find the probability that the mean height of the 75 men is less than 75 in.
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 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 flights where the mean height of the male passengers will be less than the door height
c. the probability from part (a) 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:

Step1: Analyze part (a) and (b) relevance

Part (a) gives the probability for an individual male passenger to fit through the door without bending. Part (b) gives the probability for the mean height of a group of male passengers to be less than the door - height.

Step2: Consider comfort and safety

For the comfort and safety of passengers, we are interested in whether individual male passengers can fit through the door without bending.

Answer:

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