Question

An airliner carries

250

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

nothing.

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

b. If half of the

250

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

125

men is less than

75

in.The probability is

nothing.

​(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 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​ (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?

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.

Click to select your answer(s).

Answer 1

Let X be the heights of men that are normally distributed

X~ Normal ( 69.0, 2.8)

a) P( X < 75) = P( < )

= P( z < 2.14)

= 0.9838

b) Sample size , n= 125

Let be the mean height of the 125 men

  ~ Normal ( 69.0, )

P( < 75) = P( < )

= P( z < 23.9)

= 0.9999

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

d)

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.