1. **State the problem:** We want to determine who performed better relative to their event: the runner or the swimmer. 2. **Relevant formula:** To compare performances relative to their events, we use the z-score formula: $$z = \frac{X - \mu}{\sigma}$$ where $X$ is the individual's time, $\mu$ is the mean time, and $\sigma$ is the standard deviation. 3. **Calculate the runner's z-score:** - Runner's time $X_r = 25$ minutes - Mean time $\mu_r = 28$ minutes - Standard deviation $\sigma_r = 3$ minutes $$z_r = \frac{25 - 28}{3} = \frac{-3}{3} = -1$$ 4. **Calculate the swimmer's z-score:** - Swimmer's time $X_s = 10$ minutes - Mean time $\mu_s = 12$ minutes - Standard deviation $\sigma_s = 2$ minutes $$z_s = \frac{10 - 12}{2} = \frac{-2}{2} = -1$$ 5. **Interpretation:** - A lower time is better in races, so a negative z-score means better than average. - Both the runner and swimmer have a z-score of $-1$, meaning each performed 1 standard deviation better than the mean in their respective events. **Final answer:** Both the runner and the swimmer performed equally well relative to their events, each being 1 standard deviation better than the average time.