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# 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. $\mu=1275, \sigma=6, n=1000$

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Given:

\begin{align*} \mu&=\text{Mean}=1275 \\ \sigma&=\text{Standard deviation}=6 \\ n&=\text{Sample size}=1000 \end{align*}

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

$\mu_{\overline{x}}=\mu=1275$

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:

$\sigma_{\overline{x}}=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{1000}}=\dfrac{6}{10\sqrt{10}}\approx 0.1897$

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