The article "Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength" (Quality and Reliability Engr. Intl., 2012: 387–896) considered the use of a uniform distribution with A.20 and B = 4.25 for the diameter X of a certain ype of weld (mm). 1. Determine the pdf of X and graph it. . . What is the probability that diameter exceeds 3 mm? What is the probability that diameter is within 1 mm of the mean diameter? 1. For any value a satisfying .20 < 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…

The article "Flexure of Concrete Beams Reinforced with Advanced Composite Orthogrids" (J. of Aerospace Engr, 1997: 7-15) gave the accompanying data on ultimate load (kN) for two different types of beams. Sample Sample Sample Mean Туре SD Size 33.4 2.2 Fiberglass grid 26 26 42.8 4.3 Commercial carbon grid a. Assuming that the underlying distributions are normal calculate and interpret a 99% CI for the difference between true average load for the fiberglass beams and that for the carbon beams. b. Does the upper limit of the interval you calculated in part (a) give a 99% upper confidence bound for the difference between the two us? If not, calculate such a bound. Does it strongly suggest that true average load for the carbon beams is more than that for the fiberglass beams? Explain

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 ? X  =   GPa (b) Answer the questions posed in part (a) for a sample size of  n = 256  sheets. E(X)  =   GPa ? X  =   GPa

The article “Structural Performance of Rounded Dovetail Connections Under Different Loading Conditions” (T. Tannert, H. Prion, and F. Lam, Can J Civ Eng, 2007:1600–1605) describes a study of the deformation properties of dovetail joints. In one experiment, 10 rounded dovetail connections and 10 double rounded dovetail connections were loaded until failure. The rounded connections had an average load at failure of 8.27 kN with a standard deviation of 0.62 kN. The double-rounded connections had an average load at failure of 6.11 kN with a standard deviation of 1.31 kN. Can you conclude that the mean load at failure is greater for rounded connections than for double-rounded connections?

The undergraduate grade point averages​ (UGPA) of students taking an admissions test in a recent year can be approximated by a normal​ distribution, as shown in the figure.   ​(a) What is the minimum UGPA that would still place a student in the top 15​% of​ UGPAs? ​(b) Between what two values does the middle 50​% of the UGPAs​ lie?               3.3042.6Grade point average μ=3.30 σ=0.16 x         A normal curve labeled mu = 3.30 and sigma = 0.16 is over a horizontal x-axis labeled Grade point average from 2.6 to 4 in increments of 0.35 and is centered on 3.30.       ​(a) The minimum UGPA that would still place a student in the top 15​% of UGPAs is enter your response here. ​(Round to two decimal places as​ needed.)