Answer: 0.5842

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

Author: Tanishq Prabhu