A survey found that women\'s heights are normally distributed with mean 62.8 in

Question

A survey found that women's heights are normally distributed with mean 62.8 in and standard deviation 3.3 in. The survey also found that men's heights are normaly distributed with mean 67.3 in. and standard deviation 3.5 in. Consider an executive jet that seats six with a doorway height of 55 9 in Complete parts (a) through () below a. What percentage of adult men can fit through the door without bending? The percentage of men who can fit without bending is Round to two decimal places as needed) b. Does the door design with a height of 55.9 in appear to be adequate? Why didn't the engineers design a larger door? The door design is inadequate, but because the jet is relatively small and seats only six people, a much higher door design and cost of the jet, making a larger height not practical O A. O B. The door design is adequate, because the majority of people will be able to fit without bending Thus, a larger door is not needed OC. The door design is adequate, because although many men wll not be able to fit without bending, most women will be able to ft ithout bending Thus a arger door is not needed O D. The door design is inadequate, because every person needs to be able to get into the aireraft without bending. There is no reason why this should not be . [ 1.1 : i : Vi : R. (..) ; More put mly Click to select your answer(s) ted em urces ceptance Samplin

Explanation / Answer

a)

P(X<55.9)=P(Z<(55.9-67.3)/3.5)=P(Z<-3.26)=0.06%

b)

optiomn A is correct

c) for 40 percentile crtiical z =-0.25

hence corresponding height=67.3-0.25*3.5=66.4

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