Problem
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. \[ \mu_{\bar{x}}= \]
Solution
Step 1 ：The mean of the sampling distribution (also known as the expected value of the sample mean) is equal to the population mean. In this case, the population mean is given as 101 pounds. Therefore, the mean of the sampling distribution, denoted as μx̄, is also 101 pounds.
Step 2 ：Final Answer: The mean of the sampling distribution, denoted as μx̄, is \(\boxed{101}\) pounds.
