Question

a population of values has an unknown distribution with $mu = 240.4$ and $sigma = 24.3$. you intend to draw a random sample of size $n = 173$. what is the mean of the distribution of sample means? $mu_{\bar{x}}=$ (please enter an exact answer.) what is the standard deviation of the distribution of sample means? $sigma_{\bar{x}}=$ (please report your answer accurate to 2 decimal places.) question help: video message instructor post to forum submit question

Explanation:

Step1: Recall mean of sample - means formula

The mean of the distribution of sample means $\mu_{\bar{x}}$ is equal to the population mean $\mu$. Given $\mu = 240.4$, so $\mu_{\bar{x}}=\mu$.

Step2: Recall standard - deviation of sample - means formula

The standard deviation of the distribution of sample means (also known as the standard error) is given by $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}$, where $\sigma = 24.3$ and $n = 173$.
$\sigma_{\bar{x}}=\frac{24.3}{\sqrt{173}}$
$=\frac{24.3}{13.152946}$
$\approx1.85$

Answer:

$\mu_{\bar{x}} = 240.4$
$\sigma_{\bar{x}}\approx1.85$