Question

a population of values has an unknown distribution with $mu = 186.3$ and $sigma = 75.6$. you intend to draw a random sample of size $n = 91$. 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.) > next question

Explanation:

Step1: Recall the mean of sample - means formula

The mean of the distribution of sample means $\mu_{\bar{x}}$ is equal to the population mean $\mu$. Given $\mu = 186.3$, so $\mu_{\bar{x}}=\mu$.

Step2: Recall the 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 $\sigma = 75.6$ and $n = 91$. So $\sigma_{\bar{x}}=\frac{75.6}{\sqrt{91}}$.
$\sqrt{91}\approx9.54$, then $\sigma_{\bar{x}}=\frac{75.6}{9.54}\approx7.93$.

Answer:

$\mu_{\bar{x}} = 186.3$
$\sigma_{\bar{x}}\approx7.93$