A population has parameters $$ \mu=28.4 $$ and $$ \sigma=66.2 $$. You intend to draw a random sample of size $$ n=130 $$ What is the mean of the distribution of sample means? $$ \mu_{\bar{x}}=\square $$ What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.) $$ \sigma_{\bar{x}}= $$

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To find the mean and standard deviation of the distribution of sample means (also known as the sampling distribution of the sample mean), we can use the following formulas:

1. The mean of the distribution of sample means ($$ \mu_{\bar{x}} $$) is equal to the population mean ($$ \mu $$):
   $$
   \mu_{\bar{x}} = \mu = 28.4
   $$

2. The standard deviation of the distribution of sample means ($$ \sigma_{\bar{x}} $$), also known as the standard error, is calculated using the formula:
   $$
   \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
   $$
   where $$ \sigma $$ is the population standard deviation and $$ n $$ is the sample size.

Given:
- $$ \sigma = 66.2 $$
- $$ n = 130 $$

Now, we can calculate $$ \sigma_{\bar{x}} $$:
$$
\sigma_{\bar{x}} = \frac{66.2}{\sqrt{130}} \approx \frac{66.2}{11.4018} \approx 5.80
$$

Thus, the answers are:
$$
\mu_{\bar{x}} = 28.4
$$
$$
\sigma_{\bar{x}} \approx 5.80
$$
$$ \mu_{\bar{x}} = 28.4 $$ $$ \sigma_{\bar{x}} \approx 5.80 $$

A population has parameters and . You intend to draw a random sample of size
What is the mean of the distribution of sample means?

What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)

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A population has parameters and . You intend to draw a random sample of size What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)