Question

An airliner carries 50 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.

A. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.

B. I f half of the 50 passengers are​ men, find the probability that the mean height of the 25 men is less than 75 in.

C. When considering the comfort anf safety of passengers, which result is more relevant: the probability from a or b?

why?

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

Solution:

A. If a male passenger is randomly​ selected, find the probability that he can fit through the doorway without bending.

Answer: We are required to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

B. If half of the 50 passengers are​ men, find the probability that the mean height of the 25 men is less than 75 in.

Answer: It is required to find:

Using the z-score formula, we have:

Now using the standard normal table, we have:

C. When considering the comfort and safety of passengers, which result is more relevant: the probability from a or b?

why?

Answer: The probability from part​ (a) 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?

Answer: 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.