1. State the problem. Most GMAT scores are normally distributed with mean $527$ and standard deviation $112$. We are asked: what is the probability that a randomly selected individual scores above $500$? 2. Convert to a standard normal problem. Use the z-score formula: $$z = \frac{x-\mu}{\sigma}$$ Compute the z-score for $x=500$: $$z = \frac{500-527}{112} = \frac{-27}{112} = -0.2410714286\text{ (approximately)}$$ 3. Express the probability in terms of the standard normal distribution. We want $P(X>500)=P\left(Z> -0.2410714286\right)$ where $Z$ is a standard normal random variable. By symmetry of the standard normal distribution, $P\left(Z> -0.2410714286\right)=P\left(Z<0.2410714286\right)=\Phi\left(0.2410714286\right)$. 4. Evaluate the standard normal CDF value. Using a standard normal table or calculator, $\Phi\left(0.2410714286\right) \approx 0.596053$. 5. Convert to percent and present the final answer. Multiply by 100 to convert the probability to percent: $0.596053\times 100 \approx 59.6053$. Round to two decimal places as requested to obtain the percent form without the percent symbol. Final answer: 59.61