1. **Problem Statement:** Find the area under the standard normal curve between $z=0$ and given $z$-values using the z-table. 2. **Using the z-table:** The z-table gives the area from the mean (0) to a positive z-value. For negative z-values, use symmetry: area from 0 to $-z$ equals area from 0 to $z$. 3. **Calculations for Part I:** A. For $z=-1$, area between 0 and $-1$ equals area between 0 and 1. From z-table, area(0 to 1) = 0.3413. B. For $z=2.56$, area(0 to 2.56) = 0.4948. C. For $z=-1.28$, area(0 to $-1.28$) = area(0 to 1.28) = 0.3997. 4. **Problem Statement for Part II:** Convert given scores to z-scores using formula: $$z = \frac{X - \mu}{\sigma}$$ where $\mu=48$, $\sigma=6$. 5. **Calculate z-scores and find area between them:** A. Scores 54 and 42: $$z_{54} = \frac{54-48}{6} = 1$$ $$z_{42} = \frac{42-48}{6} = -1$$ Area between $z=-1$ and $z=1$ is twice area(0 to 1): $$2 \times 0.3413 = 0.6826$$ B. Scores 52 and 60: $$z_{52} = \frac{52-48}{6} = 0.67$$ $$z_{60} = \frac{60-48}{6} = 2$$ Area between 0.67 and 2: Area(0 to 2) = 0.4772 Area(0 to 0.67) = 0.2514 Difference = $0.4772 - 0.2514 = 0.2258$ C. Scores 55 and 60: $$z_{55} = \frac{55-48}{6} = 1.17$$ $$z_{60} = 2$$ Area(0 to 2) = 0.4772 Area(0 to 1.17) = 0.3790 Difference = $0.4772 - 0.3790 = 0.0982$ D. Scores 48 and 42: $$z_{48} = 0$$ $$z_{42} = -1$$ Area between 0 and -1 is 0.3413. E. Scores 54 and 38: $$z_{54} = 1$$ $$z_{38} = \frac{38-48}{6} = -1.67$$ Area between -1.67 and 1: Area(0 to 1) = 0.3413 Area(0 to 1.67) = 0.4525 Sum = $0.3413 + 0.4525 = 0.7938$ **Final answers:** I.A: 0.3413 I.B: 0.4948 I.C: 0.3997 II.A: 0.6826 II.B: 0.2258 II.C: 0.0982 II.D: 0.3413 II.E: 0.7938