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 normally 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 (c) 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? O A. The door design is inadequate, but because the jet is relatively small and seats only sox peoplen much higher door would require major changes in the design and cost of the jet, making a larger height not practical The door design is adequate, because the majority of people will be able to fit without bending Thus, a larger door is not needed O B. O C. The door design is adequate, because aithough many men will not be able to ft without bending, most women will be able toft without bendng Thus a larger door is not needed O D. The door design is inadequate, because every person needs to be able to get into the ain c. What doorway height would allow 40% of men to fit without bening? Click to select your answer(s) implemented

Explanation / Answer

a)as z score =(X-mean)/standard deviation

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

b)

option A is correct

c)

for 40th perentile ; critical z =-0.25

hence height so that 40% men can enter without bending =67.3-0.25*3.5=66.4 in

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