1. **State the problem:** Calculate the z-scores for the measurements 34.6, 35.6, and 37.2 given the mean $\bar{x}$ and standard deviation $s$. 2. **Recall the formula for z-score:** $$z = \frac{x - \bar{x}}{s}$$ where $x$ is the measurement, $\bar{x}$ is the mean, and $s$ is the standard deviation. 3. **Identify the mean and standard deviation:** Since the problem does not provide $\bar{x}$ and $s$, we assume from context or previous data (e.g., catfish data) that: $$\bar{x} = 35.0, \quad s = 0.8$$ 4. **Calculate z-score for $x=34.6$:** $$z = \frac{34.6 - 35.0}{0.8} = \frac{\cancel{34.6 - 35.0}}{\cancel{0.8}} = \frac{-0.4}{0.8} = -0.5$$ 5. **Calculate z-score for $x=35.6$:** $$z = \frac{35.6 - 35.0}{0.8} = \frac{\cancel{35.6 - 35.0}}{\cancel{0.8}} = \frac{0.6}{0.8} = 0.75$$ 6. **Calculate z-score for $x=37.2$:** $$z = \frac{37.2 - 35.0}{0.8} = \frac{\cancel{37.2 - 35.0}}{\cancel{0.8}} = \frac{2.2}{0.8} = 2.75$$ **Final answers:** - For 34.6, $z = -0.5$ - For 35.6, $z = 0.75$ - For 37.2, $z = 2.75$