Given that 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.
Part A:
If X is the sample mean Young's modulus for a
random sample of n = 16 sheets, the sampling distribution of X
centered at 70 GPa, and the standard deviation of the X
distribution is given by [tex] \frac{1.6}{\sqrt{16}} = \frac{1.6}{4} =0.4 \ GPa[/tex]
Part B:
If X is the sample mean Young's modulus for a
random sample of n = 64 sheets, the sampling distribution of X
centered at 70 GPa, and the standard deviation of the X
distribution is given by [tex] \frac{1.6}{\sqrt{64}} = \frac{1.6}{8} =0.2 \ GPa[/tex]
