Question

a population has a mean $mu = 86$ and a standard deviation $sigma = 18$. find the mean and standard deviation of a sampling distribution of sample means with sample size $n = 81$. $mu_{\bar{x}}=square$ (simplify your answer.)

Explanation:

Step1: Recall the formula for the mean of the sampling - distribution of sample means

The mean of the sampling - distribution of sample means $\mu_{\bar{x}}$ is equal to the population mean $\mu$.
$\mu_{\bar{x}}=\mu$

Step2: Substitute the given population mean value

Given $\mu = 86$, so $\mu_{\bar{x}}=86$.

Answer:

86