Question

An airliner carries 50 passengers and has doors with a height of 72 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? (Round to four decimal places as needed.)

b. If half of the 50 passengers are men, find the probability that the mean height of the 25 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 (b) is more relevant because it shows the proportion of male passengers that will not need to bend.

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 (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.

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. There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.

C .Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

Answer 1

(a) P(X<72) = P((X-mean)/s <(72-69)/2.8) = P(Z<1.07) = 0.8577 (using z table)

(b) P(xbar<72) = P((xbar-mean)/(s/aqrt(n)) <(72-69)/(2.8/sqrt(50))) = P(Z<7.58) =1 (using z table)

(c) Option B is correct. 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) Option C is correct. Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

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