Suppose that 100 items are drawn from a population of manufactured products and the weight, X, of each item is recorded. Prior experience has shown that the weight has a non-normal probability distribution with $\mu$= 8 ounces and $\sigma$ = 3 ounces. Which of the following is true about the sampling of $\bar { X }$ ?
A)Its mean is 8 ounces.
B)Its standard error is 0.3 ounces.
C)Its shape is approximately normal.
D)All of these choices are true.

Question

Quizplus · Accepted Answer

The sampling distribution of the sample mean $\bar{X}$ will have a mean equal to the population mean ($\mu = 8$ ounces), a standard error of $\sigma/\sqrt{n} = 3/\sqrt{100} = 0.3$ ounces, and will be approximately normal due to the Central Limit Theorem, given the sample size is large (n=100).

Suppose That 100 Items Are Drawn from a Population of Manufactured