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

Range of values containing 70% of the population of x

Expert Solution & Answer
Check Mark

Answer to Problem 4.1P

Range of values 5.066x7.134

Explanation of Solution


  Assume Number of sample


  Sample Mean



  Sample MeanStandard deviation


Concept Used:

  Test Hypotheses by z test:z0=x¯μσ

Interval defined: xz0σxj x+z0σ


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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Chapter 4 Solutions

Theory and Design for Mechanical Measurements

Ch. 4 - Prob. 4.11PCh. 4 - Prob. 4.12PCh. 4 - Prob. 4.13PCh. 4 - Prob. 4.14PCh. 4 - Prob. 4.15PCh. 4 - From 19 measurements of a pressure controller, the...Ch. 4 - From 19 measurements of a pressure controller, the...Ch. 4 - When the parameters of a population are known, the...Ch. 4 - A professor grades students on a normal curve. For...Ch. 4 - Prob. 4.20PCh. 4 - 4.21 An automotive manufacturer removes the...Ch. 4 - Prob. 4.22PCh. 4 - Prob. 4.23PCh. 4 - A sampling of 409 motor shafts from a very large...Ch. 4 - During the course of a motor test, the motor rpm...Ch. 4 - A baich of rivets is tested for shear strength. A...Ch. 4 - Three independent sets of data are collected front...Ch. 4 - Prob. 4.28PCh. 4 - 4.29 An engineer measures the diameter of 20 tubes...Ch. 4 - Prob. 4.30PCh. 4 - For Problems 4.30 through 4.36. itwould be helpful...Ch. 4 - For Problems 4.30 through 4.36. itwould be helpful...Ch. 4 - For Problems 4.30 through 4.36. itwould be helpful...Ch. 4 - Prob. 4.34PCh. 4 - Prob. 4.35PCh. 4 - Prob. 4.36PCh. 4 - A manufacturer of general aircraft dry vacuum...Ch. 4 - Strength tests made on a batch of cold-drawn steel...Ch. 4 - 4.39 Determine the one-sided 95 th-percentile of...Ch. 4 - 4.40 The manufacturer of an electrical fuse claims...Ch. 4 - How many independent random measurements of a...Ch. 4 - Based on 51 measurements of a time-dependent...Ch. 4 - 4.43 Estimate the probability with which an...Ch. 4 - Prob. 4.44PCh. 4 - Prob. 4.45PCh. 4 - Prob. 4.46PCh. 4 - Prob. 4.47PCh. 4 - 4.48 A cantilever is loaded at its tip. Tip...Ch. 4 - Prob. 4.49PCh. 4 - Prob. 4.50PCh. 4 - A transducer is used to indicate the pressure of a...Ch. 4 - An engineer takes water samples from 15 lakes in...Ch. 4 - A random sample of 51 aircraft rivets is taken...Ch. 4 - Prob. 4.54PCh. 4 - Estimate the p-value for N = 16. t = 1.798...
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