Financial Risk Manager Part 1

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 $s/\sqrt{n}$.