1. **Problem statement:** You scored better than 35% of the students on an exam where scores are normally distributed with mean $\mu=62$ and standard deviation $\sigma=12$. We want to find your z-score and then determine your actual exam score. 2. **Formula and rules:** The z-score formula is: $$z=\frac{X-\mu}{\sigma}$$ where $X$ is the exam score. The z-score corresponds to the number of standard deviations a value is from the mean. 3. **Find the z-score for the 35th percentile:** The percentile rank means the cumulative area under the normal curve to the left of your score is 0.35. Using a standard normal table or calculator, the z-score for 0.35 cumulative probability is approximately: $$z \approx -0.385$$ 4. **Calculate the actual exam score $X$:** Rearranging the z-score formula: $$X = z \times \sigma + \mu$$ Substitute values: $$X = (-0.385) \times 12 + 62 = -4.62 + 62 = 57.38$$ 5. **Interpretation:** Your exam score is approximately 57.38, which means you scored better than 35% of the students. 6. **Graph description:** The normal curve is centered at 62 with standard deviation 12. The area to the left of $X=57.38$ (z = -0.385) is shaded to represent your ranking. Final answer: Your z-score is approximately $-0.385$ and your exam score is approximately $57.38$.