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 (values given in the article "Influence of Material Properties Variability on Springback and Thinning in Sheet Stamping Processes: A Stochastic Analysis

(a) If X is the sample mean Young's modulus for a random sample of
n = 16
sheets, where is the sampling distribution of X centered, and what is the standard deviation of the X distribution?

Answer 1

The sampling distribution of the sample mean Young's modulus for a random sample of aluminum alloy sheets is centered at the population mean Young's modulus of 70 GPa. The standard deviation of the sampling distribution is 0.4 GPa.

Step-by-step explanation:

The sampling distribution of the sample mean Young's modulus for a random sample of n = 16 sheets of aluminum alloy can be approximated as a normal distribution. The center of the sampling distribution, also known as the expected value, is equal to the population mean Young's modulus. In this case, the population mean Young's modulus is 70 GPa. Therefore, the sampling distribution of the sample mean Young's modulus is centered at 70 GPa.

The standard deviation of the sampling distribution, also known as the standard error of the mean, can be calculated using the formula:

Standard Error = Standard Deviation / sqrt(sample size)

For this problem, the standard deviation of the population Young's modulus is given as 1.6 GPa and the sample size is 16. Plugging in these values into the formula gives:

Standard Error = 1.6 GPa / sqrt(16) = 1.6 GPa / 4 = 0.4 GPa

Therefore, the standard deviation of the sampling distribution of the sample mean Young's modulus is 0.4 GPa.