Answered: a. If one male is randomly selected,…

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

Engineers must consider the breadths of male heads when designing motorcycle helmets. Men have head breadths that are normally distributed with a mean of 6.0 inches and a standard deviation of 1.0 inches.

a. If one male is randomly selected, find the probability that his head breadth is less than 6.2 inches.

b. Find the probability that 100 randomly selected men have a mean head breath that is less than 6.2 inches.

c. A production manager for Safeguard Helmet Company plans an initial run of 100 helmets. Seeing the result from part (b), the manager reasons that all helmets should be made for men with head breadths less than 6.2 inches because they would fit all but a few men. What is wrong with that reasoning?

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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