Question

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

Answer 1

a)
`\sigma = 0.4`

b)
`\sigma = 0.2`

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
`\sigma = 1.6`.

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

`s = (\sigma)/(√(16)) = (1.6)/(4) = 0.4`

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

`s = (\sigma)/(√(64)) = (1.6)/(8) = 0.2`