Answered: Assume that the Young’s modulus…

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

Assume that the Young’s modulus measurements of an aluminum piece produced by a casting
process follow a normal distribution with a mean of μ=74 GPa and a standard deviation of σ=1,55 GPa.
The manufacturer knows this from millions of parts that have been produced over the years.
a. What is the probability (in %) that a measurement will exceed x =(74+3) GPa?

b. What is the probability (in %) that a measurement will not exceed x =(74+1) GPa?

c. What is the probability (in %) that a measurement will be neither over x =(74-2) GPa, nor below x =
(74+4) GPa?

d. We want to expect 958 out of 1000 times that a measurement is within ± 1 GPa of the mean. What
would the standard deviation have to be for this?

Q.1 (20 %) Assume that the Young's modulus measurements of an aluminum piece produced by a casting
process follow a normal distribution with a mean of u=74 GPa and a standard deviation of o=1,55 GPa.
The manufacturer knows this from millions of parts that have been produced over the years.
a. What is the probability (in %) that a measurement will exceed x,=(74+3) GPa?

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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