A population of values has a normal distribution with $\mu=9.2$ and $\sigma=89$. You intend to draw a random sample of size $n=109$.
What is the mean of the distribution of sample means?
\[
\mu_{\bar{x}}=
\]
What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)
\[
\sigma_{\bar{x}}=
\]

Step 1 ：The mean of the distribution of sample means, also known as the expected value of the sample mean, is equal to the population mean. So, \(\mu_{\bar{x}} = \mu = 9.2\).

Step 2 ：The standard deviation of the distribution of sample means, also known as the standard error, is equal to the population standard deviation divided by the square root of the sample size. So, \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{89}{\sqrt{109}}\).

Step 3 ：Final Answer: The mean of the distribution of sample means is \(\boxed{9.2}\).

Step 4 ：Final Answer: The standard deviation of the distribution of sample means is \(\boxed{8.52}\).