An airliner carries 350 passengers and has doors with a height of 74 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts (a) through (d). a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is nothing. (Round to four decimal places as needed.) b. If half of the 350 passengers are men, find the probability that the mean height of the 175 men is less than 74 in. The probability is nothing. (Round to four decimal places as needed.) c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why? A. The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height. B. The probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height. C. The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend. D. The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.

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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Question

An airliner carries

350

passengers and has doors with a height of

in. Heights of men are normally distributed with a mean of

69.0

in and a standard deviation of

2.8

in. Complete parts (a) through (d).

a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending.

The probability is

nothing.

(Round to four decimal places as needed.)

b. If half of the

350

passengers are men, find the probability that the mean height of the

175

men is less than

in.

The probability is

nothing.

(Round to four decimal places as needed.)

c. When considering the comfort and safety of passengers, which result is more relevant: the probability from part (a) or the probability from part (b)? Why?

The probability from part (b) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.

The probability from part (a) is more relevant because it shows the proportion of flights where the mean height of the male passengers will be less than the door height.

The probability from part (b) is more relevant because it shows the proportion of male passengers that will not need to bend.

The probability from part (a) is more relevant because it shows the proportion of male passengers that will not need to bend.

d. When considering the comfort and safety of passengers, why are women ignored in this case?

A. since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodrate a greater proportion of women

B. there is no adequate reason to ignore women, a separate statistical analysis should be carried out for the case of women

C. since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. theremore, it is more important that men not have to bend than it is important that women not have to bend

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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