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.