Answer: 0.5842

## Explanation Since the standard deviation for the population is known, the standard error of the mean is calculated using the formula: $$\text{Standard Error} = \frac{\sigma}{\sqrt{n}}$$ Where: - $\sigma = 3.2$ (population standard deviation) - $n = 30$ (sample size) Plugging in the values: $$\text{Standard Error} = \frac{3.2}{\sqrt{30}} = \frac{3.2}{5.4772} \approx 0.5842$$ **Interpretation:** If we were to take multiple samples of size 30 from the U.S. coal workers population and prepare a sampling distribution of the sample means, the distribution would have: - Mean = $15.5$ (same as population mean) - Standard error = $0.5842$ **Note:** In most practical cases, the population standard deviation ($\sigma$) is unknown, so we would use the sample standard deviation ($s$) instead, with the formula $s/\sqrt{n}$.

Author: Nikitesh Somanthe