Question

determine $mu_{overline{x}}$ and $sigma_{overline{x}}$ from the given parameters of the population and sample size. $mu = 75$, $sigma = 8$, $n = 64$ $mu_{overline{x}}=square$

Explanation:

Step1: Find the mean of the sampling distribution

The mean of the sampling distribution of the sample mean \(\mu_{\bar{x}}\) is equal to the population mean \(\mu\).
\(\mu_{\bar{x}}=\mu\)
Given \(\mu = 75\), so \(\mu_{\bar{x}}=75\)

Step2: Find the standard deviation of the sampling distribution

The standard deviation of the sampling distribution of the sample mean \(\sigma_{\bar{x}}\) is given by the formula \(\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}\)
Given \(\sigma = 8\) and \(n = 64\), then \(\sigma_{\bar{x}}=\frac{8}{\sqrt{64}}=\frac{8}{8}=1\)

Answer:

\(\mu_{\bar{x}} = 75\) and \(\sigma_{\bar{x}}=1\)