The article “Monte Carlo Simulation—Tool for Better Understanding of LRFD” (J. of Structural Engr., 1993: 1586–1599) suggests that yield strength (ksi) for A36 grade steel is normally distributed with mean = 43 and standard deviation = 4.5. (a) What is the probability that yield strength is greater than 58? (b) What yield strength value separates the strongest 75% from the others?

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…

"The mean value of the design load on a foundation element is 6,000 kN, and its standard deviation is 1,200 kN. The estimated mean value of the bearing capacity is 12,000 kN, and its standard deviation 3,000 kN. If both the load and the resistance are Normally distributed, compute (a) the value of the reliability index B and (b) the probability of failure.", if the load and the resistance are positively correlated with p = 0.5.

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

what is the test stastic: p value:

An economist studying inflation in electricity prices in 2018 and 2019 believes that the average price of electricity, even after adjusting for inflation, changed between these two years. To test his claim, he samples 9 different counties and records the average price of electricity in each county from each year. He then adjusts the prices for inflation. His results are given in the following table. Test the economist's claim at the 0.02 level of significance assuming that the population distribution of the paired differences is approximately normal. Let prices in 2018 be Population 1 and prices in 2019 be Population 2. Average Residential Retail Prices of Electricity ($/kWh) 2018 2019 12.62 11.24 16.01 17.99 12.59 14.44 19.94 21.43 17.75 19.24 15.91 17.39 18.89 19.94 15.85 16.67 13.90 15.31 Copy Data Step 2 of 3: Compute the value of the test statistic. Round your answer to three decimal places.

The article "Monte Carlo Simulation Tool for Better Understanding of LRFD" suggests that yield strength (ksi) for A36 grade steel is normally distributed with = 43 and o = 4.5. (a) What is the probability that yield strength is at most 40? Greater than 60? (b) What yield strength value separates the strongest 75% from the others?

sto ave 12.72 (M4) The authors of the paper "Serum Zinc Levels of Cord Blood: Relation to Birth Weight and Gestational Period" (Journal of Trace Elements in Medicine and Biology [2015]: 180-183) car- ried out a study of zinc levels of low-birth-weight babies and normal-birth-weight babies. For a sample of 50 low- birth-weight babies, the sample mean zinc level was 17.00 and the standard error was 0.43. For a sample of 73 normal-birth-weight babies, the sample mean zinc level was 18.16 and the standard error was 0.32. Explain why the two standard errors are not the same.