An airliner carries 350 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 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 74 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​ (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.   B. 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.   C. The probability from part​ (b) 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 male passengers that will not need to bend.

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An airliner carries
350
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
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
74
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​ (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.
 
B.
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.
 
C.
The probability from part​ (b) 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 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, a design that accommodates a suitable proportion of men will necessarily accommodrate a greater proportion of women
 
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, it is more difficult for them to bend when entering the aircraft. theremore, it is more important that men not have to bend than it is important that women not have to bend 
 
 
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