### Probability and Seat Design Considerations#### Scenario: Airline Seat WidthGiven:- **Seat Width:** 16.2 inches- **Hip Breadth Distribution:** Normally distributed with a mean (\(\mu\)) of 14.2 inches and a standard deviation (\(\sigma\)) of 0.9 inches.Complete the following tasks and fill in the blanks where applicable:---**(a) Find the probability that if an individual man is randomly selected, his hip breadth will be greater than 16.2 inches.**The probability is \( \_\_\_\_\_\_\_\_\_\_ \)*(Round to four decimal places as needed.)*---**(b) If a plane is filled with 113 randomly selected men, find the probability that these men have a mean hip breadth greater than 16.2 inches.**The probability is \( \_\_\_\_\_\_\_\_\_\_ \)*(Round to four decimal places as needed.)*---**(c) Which result should be considered for any changes in seat design: the result from part (a) or part (b)?**The result from \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\) should be considered because \(\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\).---Please use these questions and templates as part of probability lessons to understand how to utilize normal distribution in practical scenarios such as ergonomics in aviation seat design.

Given: Mean = 14.2 in Standard deviation = 0.9 in ~Normal distribution

Answered: Suppose that an airline uses a seat…

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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An airliner carries 100 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 (Round to four decimal places as needed.)
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