Question

a population has parameters \\(\mu = 133\\) and \\(\sigma = 67.2\\). you intend to draw a random sample of size \\(n = 210\\).

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}} =\\)

Explanation:

Mean of the sampling distribution

Using the Sampling Distribution knowledge point

$$ \mu_{\bar{x}} = \mu = 133 $$

Standard deviation of the sampling distribution

Using the Standard Error knowledge point

$$ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} = \frac{67.2}{\sqrt{210}} \approx 4.63695 $$

Rounding the standard error

Using the Standard Error knowledge point

$$ \sigma_{\bar{x}} \approx 4.64 $$

Answer:

A population has parameters \(\mu = 133\) and \(\sigma = 67.2\). You intend to draw a random sample of size \(n = 210\).

What is the mean of the distribution of sample means?
\(\mu_{\bar{x}} =\) <blank>133</blank>

What is the standard deviation of the distribution of sample means?
(Report answer accurate to 2 decimal places.)
\(\sigma_{\bar{x}} =\) <blank>4.64</blank>