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. 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?B) Answer the questions posed in part (a) for a sample size of n - 256 sheets. C) For which of the two random samples, the one of pat(a) or the one of part (b), is x more likely to be within 1 GPa of 70 GPa? Explain. 1. 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.2. 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. 3. 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. 4. 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. Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are 70 GPa and 2.3 GPa, respectively. Suppose the distribution is normal. A) Calculate P(69 SXS 71) when n = 16. B) How likely is it that the sample mean diameter exceeds 71 when n = 367.