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

Question

An airiner carries 100 passengers and has doors with a height of 74 in. Heights of men are normaly distributed with a mean of 69.0 in and a sadard deviation of 28 in. Complete parts (a) through (d) a. If a male passenger is randomly selected, find the probablity that he can fit through the doorway without bending The probabityis Round to four decimal places as needed.) b. thalf of the 100 passengers are men,find the probablitythat the mean height of the 50 men is less than 74 in. The probablity is Round to four decimal places as needed.) cWhen considering the comfort and safety of passengers, which resuit is more relevant the probabity from part (a) or the probability fom part (b)? Why OA. The probablit from part (a)is more relevant because it shows the proportion of male passengers that will not need to bend B. The probablityfrom part (b)is more relevant because it shows the proportion of fights where the mean height of the male passengers willbe less than the door height. OC. The probability from part (a) is more relevant because it shows the proporton of fights where the mean height of the maie passengers willbe less than the door height D. The probablity from part (b)is more relevant because it shows the proporion 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? d.When considering the comfort and safety of passengers, why are women ignored in this case? OA. Since men are genealy taller than women,it is more dfficut for them to bend when entering the aircraft Thereore,it is more important that men not have to bend than iti's important that women not OB. Since men are generaly talle than women, a design that accommodates a suitable proportion af men will necessarily accommodate a greater proporian af women have to bend OC. There is no adequate reason to ignore women A separate statistical analyss should be carried out for the case of women Click to select your answerls.

Explanation / Answer

a)P(X<74)=P(Z<(74-69)/2.8)=P(Z<1.79)=0.9633 ( please try 0.9629 if this comes wrong)

b)

std error of mean =std deviaiton/sqrt(n)=2.8/sqrt(50)=0.396

hence P(Xbar<74)=P(Z<(74-69)/0.396)=P(Z<12.63)=0.0000

c)

option A is correct

d)

here we assume that mean height of women is less than men; therefore if men can fit so does women

option B is correct

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