Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for aluminum...
Fantastic news! We've Found the answer you've been seeking!
Question:
![image text in transcribed](https://s3.amazonaws.com/si.experts.images/answers/2024/05/6647b8dc941bd_4126647b8dc306f6.jpg)
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) = x = GPa GPa (b) Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) = 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 comes with a larger sample size. Ox 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. Ox 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. OX is more likely to be within 1 GPa of the mean in part (a). This is due to the increased variability of 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 = 64 sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution? E(X) = x = GPa GPa (b) Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) = 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 comes with a larger sample size. Ox 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. Ox 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. OX is more likely to be within 1 GPa of the mean in part (a). This is due to the increased variability of that comes with a smaller sample size.
Expert Answer:
Posted Date:
Students also viewed these mathematics questions
-
The lower-of-cost-or-net realizable value rule for inventory is an example of the application of: (a) the conservatism convention. (b) the historical cost principle. (c) the materiality concept. (d)...
-
Miracle Faith World Outreach, Inc., a Connecticut religious corporation, was founded by Bobby and Christine Davis in 1964. The Miracle Faith World Outreach Church started with prayer meetings in...
-
Magnetic fields are very useful in particle accelerators for "beam steering"; that is, the magnetic fields can be used to change the direction of the beam of charged particles without altering their...
-
On the first day of the current year, Griffin Company sold equipment for less than its book value. Which of the following is part of the journal entry to record the sale? a. A debit to Equipment b. A...
-
Marcellus Wallace earns $25 per hour for up to 400 units of production per day. If he produces more than 400 units per day, he will receive an additional piece rate of $0.50 per unit. Assume that his...
-
You are examining two stocks - Bassett Inc and Hound Corporation. The risk-free rate is 3% and the market risk premium is 5%. The following table provides some information. Next year's expected Beta...
-
Chaney acquires 100 % of the voting shares of Roberts on January 1, 2010 in a transaction Chaney acquires 100 % of the voting shares of Roberts on January 1, 2010 in a transaction structured as an...
-
Job - Order Costing Systems the importance of it in accounting and businnes, the practical application of how it is used, and examples of it being used and how imprtant it is?
-
The spatial part of the ground state energy eigenfunction for a one - dimensional simple harmonic oscillator is 0 ( x ) = ( m ) 1 4 e - m 2 h x 2 . Consider a quantum particle of mass m that moves in...
-
How can cultural appropriation be critically examined in contemporary artistic and commercial practices, and what frameworks exist to promote cultural respect and reciprocity ?
-
Question 4 (15 points) During the past months, a retailer shipped orders at a rate of: q(t)=3,200+25t packages per month 0t10; t being the time in months since the beginning of the year. During the...
-
What is the interrelationships among financial inclusion, financial deepening and financial intermediaries? why are these concepts so important
-
Below is a list of the relevant legislation , regulations, standard and codes of practice that may effect the preparation of financial report . outline at two provisions or principles related to each
-
A Firm intends to invest some capital for a period of 15 years; the Firm's Management considers three Options, each consisting of purchasing a machinery of a specific brand, different for each...
![Mobile App Logo](https://dsd5zvtm8ll6.cloudfront.net/includes/images/mobile/finalLogo.png)
Study smarter with the SolutionInn App