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A survey found that women's heights are normally distributed with mean 62.3 in. and standard deviation 2.3 in. The survey also found that men's heights are normally distributed with mean 68.4 in. and standard deviation 3.7 in. Consider an executive jet that seats six with a doorway height of 56.4 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 %. (Round to two decimal places as needed.)

A survey found that women's heights are normally distributed with mean 62.3 in. and standard deviation 2.3 in. The survey also found that men's heights are normally distributed with mean 68.4 in. and standard deviation 3.7 in. Consider an executive jet that seats six with a doorway height of 56.4 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 %. (Round to two decimal places as needed.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A survey found that women's heights are normally distributed with mean 62.3 in. and standard deviation 2.3 in. The survey also found that men's heights are normally distributed with mean 68.4 in. and standard deviation 3.7 in. Consider an executive jet that seats six with a doorway height of 56.4 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 %. (Round to two decimal places as needed.) b. Does the door design with a height of 56.4 in. appear to be adequate? Why didn't the engineers design a larger door? O A. 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. O B. 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. O C. 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. O D. The door design is adequate, because the majority of people 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 (Round to one decimal place as needed.) in.
Transcribed Image Text:A survey found that women's heights are normally distributed with mean 62.3 in. and standard deviation 2.3 in. The survey also found that men's heights are normally distributed with mean 68.4 in. and standard deviation 3.7 in. Consider an executive jet that seats six with a doorway height of 56.4 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 %. (Round to two decimal places as needed.) b. Does the door design with a height of 56.4 in. appear to be adequate? Why didn't the engineers design a larger door? O A. 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. O B. 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. O C. 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. O D. The door design is adequate, because the majority of people 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 (Round to one decimal place as needed.) in.
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