1. **Problem Statement:** Find and illustrate the area under the standard normal curve for $z = 2.03$. 2. **Understanding the Standard Normal Distribution:** The standard normal distribution is a bell-shaped curve centered at 0 with a standard deviation of 1. 3. **Using the Z-Table:** The Z-table gives the area between the mean (0) and a positive z-value. For $z=2.03$, find the area from 0 to 2.03. 4. **Look up the value:** From the Z-table, the area between 0 and 2.03 is approximately $0.4788$. 5. **Interpretation:** This means the probability that $Z$ lies between 0 and 2.03 is $0.4788$. 6. **Calculate total area from the left:** Since the total area to the left of 0 is $0.5$, the total area to the left of $z=2.03$ is $$0.5 + 0.4788 = 0.9788$$ 7. **Final answer:** The area under the curve from the far left up to $z=2.03$ is $0.9788$. This area represents the cumulative probability $P(Z \leq 2.03) = 0.9788$.