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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 (J. of Advanced Manuf Tech, 2010 117-134 Ca is the sample mean Young's modulus for a random sample of n-64 sheets, where is the sampling distribution of centered, and what is the standard deviation of the distribution? (b) Answer the questions posed in part (a) for a sample size of -256 sheets. EXO-L 1₂ that comes with a smaller sample size. (c) For which of the two random samples, the one of part (a) or the one of part (b), is more likely to be within 1 GPa of 70 GPa? Explain your reasoning Os more likely to be within 1 GPa of the mean in part (a). This is due to the decreased variability of is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of Os more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of that comes with a larger sample size. that comes with a larger sample size

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 (J. of Advanced Manuf Tech, 2010 117-134 Ca is the sample mean Young's modulus for a random sample of n-64 sheets, where is the sampling distribution of centered, and what is the standard deviation of the distribution? (b) Answer the questions posed in part (a) for a sample size of -256 sheets. EXO-L 1₂ that comes with a smaller sample size. (c) For which of the two random samples, the one of part (a) or the one of part (b), is more likely to be within 1 GPa of 70 GPa? Explain your reasoning Os more likely to be within 1 GPa of the mean in part (a). This is due to the decreased variability of is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of Os more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of that comes with a larger sample size. that comes with a larger sample size

MATLAB: An Introduction with Applications
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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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 = 64 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) = GPa GPa ox= (b) Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) = ox GPa GPa (c) For which of the two random samples, the one of part (a) or the one of part (b), is more likely to be within 1 GPa of 70 GPa? Explain your reasoning. O X is more likely to be within 1 GPa of the mean in part (a). This is due to the decreased variability of X that comes with a smaller sample size. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of that comes with a larger sample size. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of X that comes with a larger sample size. O X is more likely to be within 1 GPa of the mean in part (a). This is due to the increased variability of X that comes with a smaller sample size.
Transcribed Image Text: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 = 64 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) = GPa GPa ox= (b) Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) = ox GPa GPa (c) For which of the two random samples, the one of part (a) or the one of part (b), is more likely to be within 1 GPa of 70 GPa? Explain your reasoning. O X is more likely to be within 1 GPa of the mean in part (a). This is due to the decreased variability of X that comes with a smaller sample size. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the decreased variability of that comes with a larger sample size. O X is more likely to be within 1 GPa of the mean in part (b). This is due to the increased variability of X that comes with a larger sample size. O X is more likely to be within 1 GPa of the mean in part (a). This is due to the increased variability of X that comes with a smaller sample size.
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