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 the increased variability of X that comes with a smaller sample size.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 comes with a larger sample size. 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.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. 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%3DGPa(b) Answer the questions posed in part (a) forsample size of n = 64 sheets.E(X) =GPaGPa(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.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.O 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 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 decreased variability of X that comes with a smaller sample size.

Answered: Image /qna-images/answer/be697032-5819-4c7b-ba9b-a456c4506a7f.jpg

Answered: Young's modulus is a quantitative…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

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 the increased variability of X that comes with a smaller sample size.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 comes with a larger sample size. 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.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.

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
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.
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.
O 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 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 decreased variability of X that comes with a smaller sample size.

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 + ...

Expert Solution

Step 1

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here