## 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. $\mu=45, \sigma=15, n=100$

Solution

VerifiedAnswered 10 months ago

Answered 10 months ago

Step 1

1 of 2Given:

$\begin{align*} \mu&=\text{Mean}=45 \\ \sigma&=\text{Standard deviation}=15 \\ n&=\text{Sample size}=100 \end{align*}$

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

$\mu_{\overline{x}}=\mu=45$

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:

$\sigma_{\overline{x}}=\dfrac{\sigma}{\sqrt{n}}=\dfrac{15}{\sqrt{100}}=\dfrac{15}{10}=1.5$

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