Answered: The ultimate tensile strength of an…

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

The ultimate tensile strength of an aircraft bolt has mean 20 kN and is believed to be (at least

approximately) normally distributed. The manufacturer wishes to control the quality of the

aircraft bolt and measures the strength of 10 bolt samples. A sample standard deviation of

2 kN is observed, and it is assumed that the measurements are independent. Based on the

information provided, for any ten randomly selected independent bolt samples,

a) the sample mean will not be less than what value with 95% probability?

b) what is the probability that the sample mean exceeds 18 kN (suppose that specifications

for the aircraft bolt require that the ultimate tensile strength be at least 18 kN)?

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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