## Related questions with answers

Question

A population has a mean $\mu$ and a standard deviation $\sigma$. Find the mean and standard deviation of the sampling distribution of sample means with sample size n. $\mu=150, \sigma=25, n=50$

Solution

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1 of 2Given:

$\begin{align*} \mu&=\text{Mean}=150 \\ \sigma&=\text{Standard deviation}=25 \\ n&=\text{Sample size}=50 \end{align*}$

The $\textbf{mean}$ of the sampling distribution of the sample mean is equal to the population mean:

$\mu_{\overline{x}}=\mu=150$

The $\textbf{standard deviation}$ of the sampling distribution of the sample mean is equal to the population standard deviation divided by the square root of the sample size:

$\sigma_{\overline{x}}=\dfrac{\sigma}{\sqrt{n}}=\dfrac{25}{\sqrt{50}}=\dfrac{5}{\sqrt{2}}\approx 3.5355$

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