Question

A survey found that​ women's heights are normally distributed with mean

63.3 in63.3 in.

and standard deviation

2.3 in2.3 in.

The survey also found that​ men's heights are normally distributed with mean

68.8 in68.8 in.

and standard deviation

3.1 in3.1 in.

Consider an executive jet that seats six with a doorway height of

56.4 in56.4 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

nothing​%.

​(Round to two decimal places as​ needed.)

b. Does the door design with a height of

56.456.4

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

A.

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

B.

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

C.

The door design is​ adequate, because the majority of people will be able to fit without bending.​ Thus, a larger door is not needed.

D.

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

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

The doorway height that would allow​ 40% of men to fit without bending is

nothing

in.

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

Answer 1