ck 4.2
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A population has a mean $\mu =80$ and a standard deviation $\sigma =8$. Find the mean and standard deviation of a sampling distribution of sample means with sample size $n=64$.
${\mu }_{\dot{-}}=◻$ (Simplify your answer.)
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Step 1 ：A population has a mean of $\mu =80$ and a standard deviation of $\sigma =8$. We are asked to find the mean and standard deviation of a sampling distribution of sample means with sample size $n=64$.

Step 2 ：The mean of the sampling distribution of sample means is equal to the mean of the population. Therefore, ${\mu }_{\dot{-}}=\mu =80$.

Step 3 ：The standard deviation of the sampling distribution of sample means is given by the formula ${\sigma }_{\dot{-}}=\frac{\sigma }{\sqrt{n}}$, where $\sigma$ is the standard deviation of the population and $n$ is the sample size.

Step 4 ：Substituting the given values into the formula, we get ${\sigma }_{\dot{-}}=\frac{8}{\sqrt{64}}$.

Step 5 ：Solving the above expression, we find that ${\sigma }_{\dot{-}}=1.0$.

Step 6 ：Therefore, the mean and standard deviation of the sampling distribution of sample means with sample size $n=64$ are ${\mu }_{\dot{-}}=80$ and ${\sigma }_{\dot{-}}=1.0$ respectively.

Step 7 ：$\boxed{{\displaystyle {\mu }_{\dot{-}}=80,{\sigma }_{\dot{-}}=1.0}}$