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 is the sample mean Young's modulus for a random sample of n = 16 sheets, where is the sampling distribution of centered, and what is the standard deviation of the distribution?
b. Answer the questions posed in part (a) for a sample size of n 5 64 sheets.
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.