.. ..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 and1.6 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 AdvancedManuf. 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) for a sample 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.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 (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 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.Need Help?Read ItMacBook Pro"0.3"&!@#$12478}PQWERTYU%3D

(a) The sampling distribution of X¯ centered is, EX¯=μ=70 Thus, the sampling distribution of X¯…

(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 GPa (b) Answer the questions posed in part (a) for a sample size of n = 64 sheets. E(X) = GPa GPa

(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 GPa (b) Answer the questions posed in part (a) for a sample size of n = 64 sheets. E(X) = GPa GPa

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 30E

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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 (b) Answer the questions posed in part (a) for a sample size of n = 256 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 increased variability of X that comes with a…
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) ох = GPa GPa (b) Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) GPa GPa ох = (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 (b). This is due to the increased 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 GPa x = (b) Answer the questions posed in part (a) for a sample size of n = 64 sheets. E(X) GPa GPa ox = (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 (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)). | 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? EX) = GPa GPa J Answer the questions posed in part (a) for a sample size of n = 256 sheets. E(X) = GPa GPa For which of the two random samples, the one 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 (b). This is due to the increased variability of X that comes with a larger…
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…
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…
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
Young'smodulus 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 1.6GPa, respectively (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis" (Intl.]. of.4dvanced Manuf. Tech,2010:117-134)) a. If x̄ is the sample mean Young's modulus for a random sample of n= 16 sheets, where is the sampling distribution of x̄ centered, and what is the standard deviation of the x̄ distribution? b. Answer the questions posed in part (a) for a sample size of n= 64 sheets. c. For which of the two random samples, the one of part (a) or the one of part (b), is x̄ more likely to be within 1GPa of 70 GPa? Explain your reasoning.
widely used as dielectrics and coolants in electrical systems in the past. They were found to be a major environmental contaminant in the 1960s. In a study, the mean PCB content at each of thirteen sites was reported for the years 1982 and 1996 (from “The ratio of DDE to PCB concentrations in Great Lakes herring gull eggs and its use in interpreting contaminants data”, Journal of Great Lakes Research 24 (1): 12-31, 1998). The data are below.Site:12345678910111213198261.4864.4745.5059.7058.8175.9671.5738.0630.5139.7029.7866.8963.93199613.9918.2611.2810.0221.0017.3628.207.3012.809.4112.6316.8322.74(a) Which test would be more appropriate in this case: a t-test for the difference between two population means, or a paired t-test? Why?(b) Do the data provide sufficient evidence to support the claim that the mean PCB level has decreased in the region? Be sure to check all assumptions, write the null and alternative hypotheses, calculate the appropriate test statistic, calculate the p-value,…
Lemons and Car Crashes Listed below are annual data for various years. The data are weights (metric tons) of lemons imported from Mexico and U.S. car crash fatality rates per 100,000 population [based on data from “The Trouble with QSAR (or How I Learned to Stop Worrying and Embrace Fallacy),” by Stephen Johnson, Journal of Chemical Information and Modeling, Vol. 48, No. 1]. Is there sufficient evidence to conclude that there is a linear correlation between weights of lemon imports from Mexico and U.S. car fatality rates? Do the results suggest that imported lemons cause car fatalities?
Vehicle speed on a particular bridge in China can be modeled as normally distributed (“Fatigue Reliability Assessment for Long-Span Bridges under Combined Dynamic Loads from Winds and Vehicles,” J. of Bridge Engr., 2013: 735–747).a. If 5% of all vehicles travel less than 39.12 m/h and 10% travel more than 73.24 m/h, what are the mean and standard deviation of vehicle speed? [Note: The resulting values should agree with those given in the cited article.]b. What is the probability that a randomly selected vehicle’s speed is between 50 and 65 m/h?c. What is the probability that a randomly selected vehicle’s speed exceeds the speed limit of 70 m/h?
An article in Plant Disease, "Effect of Nitrogen and Potassium Fertilizer Rates on Severity of Xanthomonas Blight of Syngonium Podophyllum" (1989, Vol. 73, No. 12, pp. 972-975) showed the effect of the variable nitrogen and potassium rates on the growth of "White Butterfly" and the mean percentage of disease. Data representative of that collected in this experiment is provided in the following table. Potassium (mg/pot/wk) Nitrogen (mg/pot/wk) 30 90 120 50 60.8 60.8 45.5 43.0 60.0 58.4 150 54.4 56.1 53.8 51.6 34.5 35.5 250 42.9 40.0 36.1 37.9 33.0 33.3 (a) Use the analysis of variance to test the appropriate hypotheses with a = 0.05. The effect of the variable nitrogen significant, the effect of the potassium rates significant, the interaction between the variable nitrogen and potassium rates significant. (b) Graphically analyze the residuals from this experiment. The residuals acceptable. (c) Estimate the appropriate variance component. Round your answers to 2 decimal places. Source…