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.

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

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

a)

b)

Step-by-step explanation:

The standard deviation of the sample is the standard deviation of population divided by the square root of the length of the sample.

In this problem, we have that:

Suppose that for aluminum alloy sheets of a particular type, its mean value and standard deviation are 70 GPa and 1.6 GPa, respectively. This means that .

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

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