Question

Statistics problem. I have a homework that I am having trouble with.

Answer 1

The formula for the mean and standard deviation of a sampling distribution is

`\begin{gathered} \mu_{\bar{x}}=\mu \\ and\text{ } \\ \sigma_{\bar{x}}=(\sigma)/(√(n)) \end{gathered}`

Now, on putting the values we have

`\begin{gathered} \sigma=10\text{ and }\mu=126 \\ Then,\text{ } \\ (i).\text{ n=26} \\ \begin{equation*} \mu_{\bar{x}}=126 \end{equation*} \\ and \\ \sigma_{\bar{x}}=(10)/(√(26)) \\ (\imaginaryI\imaginaryI)\text{ n = 38} \\ \begin{equation*} \mu_{\bar{x}}=126 \end{equation*} \\ and \\ \sigma_{\bar{x}}=(10)/(√(38)) \end{gathered}`

Hence, this is the required answer.