An airliner carries 100 passengers and has doors with a height of 74 in. Heights

Question

An airliner carries 100 passengers and has doors with a height of 74 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 100 passengers are men, find the probability that the mean height of the 50 men is less than 74 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? OA. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend O B. The probability from part (b) is more relevant because it shows the proportion of fights where the mean height of the male passengers will be less than the door height OC. 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 0 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?

Explanation / Answer

Result:

a).

z value for 74, z =(74-69)/2.8 =1.79

P( x <74) = P( z <1.79)

=0.9633

b).

standard error = sd/sqrt(n) =2.8/sqrt(50) =0.3960

z value for 74, z =(74-69)/0.3960=12.63

P( mean x <74) = P( z < 12.63)

=0.0000

c).

A). the probability of 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.

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