Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 101 pounds and a standard deviation of 39.8 pounds. Random samples of size 18 are drawn from this population and the mean of each sample is determined. \[ \mu_{\bar{x}}=101 \] \[ \sigma_{\bar{x}}=\square \text { (Round to three decimal places as needed.) } \]

Step 1 ：The problem provides us with the following information: the mean (μ) of the per capita consumption of red meat is 101 pounds, the standard deviation (σ) is 39.8 pounds, and the sample size (n) is 18.

Step 2 ：We are asked to find the mean (μx̄) and the standard error of the mean (σx̄) of the sampling distribution.

Step 3 ：According to the Central Limit Theorem, the mean of the sampling distribution (μx̄) is equal to the population mean (μ). Therefore, \(\mu_{\bar{x}}=101\).

Step 4 ：The standard error of the mean (σx̄) can be calculated using the formula: \(\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}\), where σ is the standard deviation of the population and n is the size of the sample.

Step 5 ：Substituting the given values into the formula, we get \(\sigma_{\bar{x}} = \frac{39.8}{\sqrt{18}}\).

Step 6 ：Calculating the above expression, we find that \(\sigma_{\bar{x}}\) is approximately 9.381.

Step 7 ：Final Answer: The standard error of the mean is \(\boxed{9.381}\) pounds.