Question

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 (

Answer 1

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 $\frac{1.6}{\sqrt{16}} = \frac{1.6}{4} =0.4 \ GPa$



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 $\frac{1.6}{\sqrt{64}} = \frac{1.6}{8} =0.2 \ GPa$