Question 1, 8.1.9
Part 1 of 2
K
Determine $\mu_{\bar{x}}$ and $\sigma_{\bar{x}}$ from the given parameters of the population and sample size.
\[
\mu=79, \sigma=6, n=36
\]
\[
\mu_{\bar{x}}=\square
\]
Answer
Final Answer: \(\mu_{\bar{x}} = \boxed{79}\) and \(\sigma_{\bar{x}} = \boxed{1}\)
Step 1 ：The problem provides the population mean (\(\mu\)) as 79, the population standard deviation (\(\sigma\)) as 6, and the sample size (\(n\)) as 36.
Step 2 ：The mean of the sample mean (\(\mu_{\bar{x}}\)) is equal to the population mean (\(\mu\)). Therefore, \(\mu_{\bar{x}} = \mu = 79\).
Step 3 ：The standard deviation of the sample mean (\(\sigma_{\bar{x}}\)) is equal to the population standard deviation (\(\sigma\)) divided by the square root of the sample size (\(n\)). Therefore, \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{36}} = 1\).
Step 4 ：Final Answer: \(\mu_{\bar{x}} = \boxed{79}\) and \(\sigma_{\bar{x}} = \boxed{1}\)
