Please show and explain the steps! 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 MaterialProperties 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) =GPaGPa(b) Answer the questions posed in part (a) for a sample size of n = 256 sheets.E(X) =GPaGPa= %o(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 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.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 (a). This is due to the increased variability of X that comes with a smaller sample size.

The Expected value (mean) of the sampling distribution of the sample mean (). The standard deviation of the sampling distribution of the sample mean (). Plug in all the values in the formula, we getThe Expected value (mean) of the sampling distribution of the sample mean (). The standard deviation of the sampling distribution of the sample mean (). Plug in all the values in the formula, we get