Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
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Textbook Question
Chapter 4.1, Problem 7E
The article “Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength” (Quality and Reliability Engr. Intl., 2012: 887–896) considered the use of a uniform distribution with A = .20 and B = 4.25 for the diameter X of a certain type of weld (mm).
a. Determine the
b. What is the probability that diameter exceeds 3 mm?
c. What is the probability that diameter is within 1 mm of the
d. For any value a satisfying .20 < a < a + 1 < 4.25, what is P(a < X < a + 1)?
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a. Construct a stem-and-leaf display of the data.b. What is a typical, or representative, flow rate?c. Does the display appear to be highly concentrated orspread out?d. Does the distribution of values appear to…
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Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and
1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of Advanced
Manuf. Tech., 2010: 117-134)).
(a) If X is the sample mean Young's modulus for a random sample of n = 16 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution?
E(X)
GPa
%3D
GPa
(b) Answer the questions posed in part (a) for a sample size of n = 64 sheets.
E(X) =
GPa
GPa
(c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 1 GPa of 70 GPa? Explain your reasoning.
X is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of X that…
Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl. J. of Advanced Manuf. Tech., 2010: 117–134)).
(a) If X is the sample mean Young's modulus for a random sample of
n = 16
sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution?
E(X)
=
GPa
? X
=
GPa
(b) Answer the questions posed in part (a) for a sample size of
n = 64
sheets.
E(X)
=
GPa
? X
=
GPa
(c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 1 GPa of 70 GPa? Explain your reasoning.
X is more likely to be within 1 GPa of the mean in part (a). This is due to…
Chapter 4 Solutions
Probability and Statistics for Engineering and the Sciences
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