1. **Problem:** Find the area between $z=2$ and $z=3$ using the z-table. 2. **Formula and rules:** The area between two z-values $z_1$ and $z_2$ on the standard normal curve is given by the difference of their cumulative probabilities: $$\text{Area} = P(z_2) - P(z_1)$$ where $P(z)$ is the cumulative area from the far left up to $z$. 3. **Step-by-step solution:** - From the z-table, find $P(3)$ and $P(2)$. - Typically, $P(3) \approx 0.9987$ and $P(2) \approx 0.9772$. - Calculate the area: $$\text{Area} = 0.9987 - 0.9772 = 0.0215$$ 4. **Interpretation:** This means about 2.15% of the data lies between $z=2$ and $z=3$ under the normal curve. 5. **Sketch description:** - Draw a bell-shaped normal curve centered at 0. - Mark vertical lines at $z=2$ and $z=3$ on the horizontal axis. - Shade the area under the curve between these two lines to represent the calculated area. This completes the solution for the first problem.