Question

An airliner carries

350

passengers and has doors with a height of

72

in. Heights of men are normally distributed with a mean of

69

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

nothing.

​(Round to four decimal places as​ needed.)

b. If half of the

350

passengers are​ men, find the probability that the mean height of the

175

men is less than

72

in.

The probability is

​(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.

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, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

C.

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.

Answer 1