Find the mean and standard error of the mean of the sampling distribution. Then sketch a graph of the sampling distribution
The prices of photo printers on a website are normally distributed with a mean of $\mathrm{\$}225$ and a standard deviation of $68. Random samples of size 23 are drawn from this population and the mean of each sample is determined
The mean of the distribution of sample means is 225
The standard deviation of the distribution of sample means is
(Type an integer or decimal rounded to three decimal places as needed.)

Step 1 ：The prices of photo printers on a website are normally distributed with a mean of $225andastandarddeviationof$68. Random samples of size 23 are drawn from this population and the mean of each sample is determined.

Step 2 ：The mean of the distribution of sample means is 225.

Step 3 ：The standard deviation of the distribution of sample means, also known as the standard error, can be calculated using the formula: $${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}$$ where ${\sigma }_{\overline{x}}$ is the standard deviation of the distribution of sample means (standard error), $\sigma$ is the standard deviation of the population, and $n$ is the size of the samples.

Step 4 ：In this case, $\sigma =\$68$ and $n=23$. We can substitute these values into the formula to find the standard error.

Step 5 ：Substituting the given values into the formula, we get $${\sigma }_{\overline{x}}=\frac{68}{\sqrt{23}}$$

Step 6 ：Calculating the above expression, we get ${\sigma }_{\overline{x}}=14.179$

Step 7 ：Final Answer: The standard deviation of the distribution of sample means is $\boxed{{\displaystyle 14.179}}$.