1. The problem is to find the area under the standard normal curve from Z=0 to Z=1.35. 2. Using the table, split 1.35 into 1.3 (row) and 0.05 (column). 3. The area from 0 to 1.35 is approximately 0.4332 (from row 1.3, col 0.05). 4. So, area from Z=0 to Z=1.35 equals **0.4332**. 1. Find the area for P(-2.05 ≤ Z ≤ 1.96). 2. First find area from 0 to 1.96: row 1.9, col 0.06 is 0.4750 (approx). 3. Then find area from 0 to 2.05: row 2.0, col 0.05 is 0.4798. 4. Area from -2.05 to 0 is same as from 0 to 2.05 by symmetry, 0.4798. 5. Total area: 0.4798 (left) + 0.4750 (right) = **0.9548**. 1. Find P(Z ≤ -1.47). 2. Area from 0 to 1.47: row 1.4, col 0.07 approx 0.4292. 3. For negative Z: P(Z ≤ -1.47) = 0.5 - area from 0 to 1.47 = 0.5 - 0.4292 = **0.0708**. 1. Area to the left of Z = 2.01. 2. Area from 0 to 2.01: row 2.0, col 0.01 approx 0.4778. 3. Total area P(Z ≤ 2.01) = 0.5 (left half) + 0.4778 = **0.9778**. 1. Find P(-3.1 ≤ Z ≤ -1.27). 2. Area from 0 to 3.1: row 3.1, col 0.00 approx 0.49903. 3. Area from 0 to 1.27: row 1.2, col 0.07 approx 0.3980. 4. For negative Z, area between -3.1 and -1.27 = (area to left of -1.27) - (area to left of -3.1). 5. P(Z ≤ -1.27) = 0.5 - 0.3980 = 0.1020 6. P(Z ≤ -3.1) = 0.5 - 0.49903 = 0.00097 7. Difference: 0.1020 - 0.00097 = **0.1010**. Final answers: 1. 0.4332 2. 0.9548 3. 0.0708 4. 0.9778 5. 0.1010 This completes the calculation of areas under the normal curve for the given Z-values by using the provided standard normal table.