1. **State the problem:** We are given a population mean $\mu = 50$, standard deviation $\sigma = 4$, and a score $X = 58$. We need to find the z-value corresponding to this score. 2. **Formula used:** The z-value is calculated by the formula: $$z = \frac{X - \mu}{\sigma}$$ This formula tells us how many standard deviations the score $X$ is away from the mean $\mu$. 3. **Substitute the values:** $$z = \frac{58 - 50}{4}$$ 4. **Simplify the numerator:** $$z = \frac{8}{4}$$ 5. **Simplify the fraction:** $$z = \frac{\cancel{8}}{\cancel{4} \times 2} = 2$$ 6. **Interpretation:** The z-value is 2, meaning the score 58 is 2 standard deviations above the mean. **Final answer:** $$z = 2$$