Answered: What percentage of adult men can fit…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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

63.6 in. and standard deviation 3.5 in. The survey also found that men's heights are normally distributed with mean 67.5 in. and standard deviation 3.6 in. Consider an executive jet that seats six with a doorway height of 55.9 in.

a. What percentage of adult men can fit through the door without bending?

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?

A.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.

B.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.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 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.

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

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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