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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 GPa 0x b Answer the questions posed in part a for a sample size of n 256 sheets E X ox GPa GPa 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 OX 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 OX 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 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 OX 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

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