a. If a male passenger is randomly selected, find the probability that he can fit through the doorway without bending. The probability is _. (Round to four decimal places as needed.) b. If half of the 300 passengers are men, find the probability that the mean height of the 150 men is less than 70 in. The probability is . (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 male passengers that will not need to bend. 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 (a) is more relevant because it shows the proportion of male passengers that will not need to bend. D. 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. 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 accommodate a greater proportion of women. B. Since men are generally taller than women, it is more difficult for them to bend when entering the aircraft. Therefore, it is more important that men not have to bend than it is important that women not have to bend. C.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

An airliner carries 300passengers and has doors with a height of 70
in. Heights of men are normally distributed with a mean of 69.0
in and a standard deviation of 2.8 in.

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

The probability is _____. (Round to four decimal places as needed.)

b. If half of the 300 passengers are men, find the probability that the mean height of the 150 men is less than 70 in.

The probability is ____. (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 male passengers that will not need to bend.

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

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.

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

Since men are generally taller than women, a design that accommodates a suitable proportion of men will necessarily accommodate a greater proportion of women.

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

There is no adequate reason to ignore women. A separate statistical analysis should be carried out for the case of women.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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