Confirm that the two formulas in the central limit theorem hold true for the population containing the elements {1, 5, 10}. First, compute the population mean and standard deviation for the data set. Next, create a list of all nine of the possible two-element samples that can be created with replacement: {1, 1}, {1, 5}, etc. For each of the nine, compute the sample mean. Now find the mean of the sample means. Does it equal the population mean? Compute the standard deviation of the sample means. Does it equal the population standard deviation, divided by the square root of n?

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