Answered: There are many engineering properties…

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

There are many engineering properties which cannot be negative, and so cannot be modeled

using a normal distribution (since the normal distribution always has some probability of being

negative). One such engineering property is the tensile strength of glue – it doesn’t make

sense that a glue’s tensile strength would be negative. A common nonnegative

distribution

used in engineering models is the lognormal, which is strictly nonnegative

and has a simple

relationshipwith the normal distribution. Suppose that a particular type of glue is is lognormally

distributed with mean 10 MPa and coefficient of variation 25%. If a random sample of this

glue is tested,

a) What is the probability that its tensile strength will lie between 6 and 12 MPa?
b) Suppose that the design tensile strength of this glue is its 10th percentile. What is this
glue's design tensile strength? (Note: the 10th percentile is the value, x10, such that
P[X < x1o] = 0.1)

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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