finding the mean of the sample mean

Question

given that the population of the quarters has a mean weight of 5.67 g and a standard deviation of 1.34 g what is the mean of the sample means? (use central limit theorem) My issue if I am even supposed to be using this formula it requires to know what n is how do I know what n is since it doesn't list a sample size. it is not given in the question or is the mean of the sample mean the same number 5.67 help! the second part is what is the standard error?

Answer 1

If we're working with the sample means $\bar{X}$, then $$\begin{align} \mu_{\bar{X}} &= \mu \\ \sigma_{\bar{X}} &= \dfrac{\sigma}{\sqrt{n}}\text{.} \end{align}$$ Judging by your questions, I'm guessing that this is not a class where you prove these formulas, so I'm not showing the proofs of these formulas.

$\mu$, recall, is the population mean, so $\mu_{\bar{X}} = \mu = 5.67$.

The standard error is $\sigma_{\bar{X}}$, with the sample standard deviation used in place of the population standard deviation. Since $\sigma_{\bar{X}} = \dfrac{\sigma}{\sqrt{n}}$, the standard error is $\dfrac{S}{\sqrt{n}}$.