Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
Question
Chapter 4, Problem 4.1P
To determine

## Range of values containing 70% of the population of x

Expert Solution & Answer

## Answer to Problem 4.1P

Range of values 5.066x7.134

### Explanation of Solution

Given:

Assume Number of sample

N=1000

Sample Mean

x¯=6.1

units

Sample MeanStandard deviation

σ=1

Concept Used:

Test Hypotheses by z test:z0=x¯μσ

Interval defined: xz0σxj x+z0σ

Calculation:

As per the given problem

Assuming that the sample data is adequately large such that its population behaves as an infinite population, so it needs to solve the integral

p(z0)=12π0z1eβ2/2dβ ............(1)

Over the interval defined by z0 . Table 4.3 lists the solutions for this integral. Using Table 4.3 for, we find p(z0)=0.35 ,  Then the value of z0 =1.034.We should expect that 70% of the xjvalues lie in the interval given by

xz0σxj x+z0σ

6.11.034xj 6.1+1.034

5.066xj 7.134

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