A survey found that​ women's heights are normally distributedwith mean 62.3 in. and standard deviation 3.6 in. The survey alsofound that​ men's heights are normally distributed with mean 67.7in. and standard deviation 3.3 in. Consider an executive jet thatseats six with a doorway height of 55.7 in. Complete parts​ (a)through​ (c) below.

a. What percentage of adult men can fit through the doorwithout​ 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

55.755.7

in. appear to be​ adequate? Why​ didn't the engineers design alarger​ door?

A.

The door design is​ inadequate, but because the jet isrelatively small and seats only six​ people, a much higher doorwould require major changes in the design and cost of the​ jet,making a larger height not practical.

B.

The door design is​ adequate, because the majority of peoplewill be able to fit without bending.​ Thus, a larger door is notneeded.

C.

The door design is​ adequate, because although many men will notbe able to fit without​ bending, most women will be able to fitwithout bending.​ Thus, a larger door is not needed.

D.

The door design is​ inadequate, because every person needs to beable to get into the aircraft without bending. There is no reasonwhy this should not be implemented.

c. What doorway height would allow​ 40% of men to fit without​bending?

The doorway height that would allow​ 40% of men to fit withoutbending is

__

in.

​(Round to one decimal place as​ needed.)