1. **State the problem:** We want to find the percentile rank of a score $X=84$ on a nationwide aptitude test where scores are normally distributed with mean $\mu=80$ and standard deviation $\sigma=15$. 2. **Formula and explanation:** The percentile rank corresponds to the cumulative probability $P(X \leq 84)$ under the normal distribution. We use the standard normal variable $Z$ defined by: $$Z = \frac{X - \mu}{\sigma}$$ This converts the score to a standard normal distribution with mean 0 and standard deviation 1. 3. **Calculate the Z-score:** $$Z = \frac{84 - 80}{15} = \frac{4}{15} \approx 0.267$$ 4. **Find the cumulative probability:** Using standard normal distribution tables or a calculator, find $P(Z \leq 0.267)$. This value is approximately 0.6057. 5. **Interpretation:** The percentile rank of a score of 84 is about 60.57%, meaning approximately 60.57% of test takers scored below 84. **Final answer:** The percentile rank of a score of 84 is approximately **60.57%**.