1. **Problem Statement:** Find the area of the standard normal distribution between z = -0.67 and z = 0 (Check Your Progress 3). Find the area of the standard normal distribution to the left of z = -1.47 (Check Your Progress 4). 2. **Step for Check Your Progress 3:** The standard normal distribution is symmetric about z = 0. Therefore, the area between z = -0.67 and z = 0 is equal to the area between z = 0 and z = 0.67. 3. **Find the area from z = 0 to z = 0.67:** Using the standard normal table, the area between 0 and 0.67 is approximately 0.2514. 4. **Final area for z = -0.67 to 0:** Thus, the area between z = -0.67 and z = 0 is also **0.2514**. 5. **Step for Check Your Progress 4:** To find the area to the left of z = -1.47, use symmetry and the standard normal table. 6. **Find the area from 0 to 1.47:** The table shows the area between 0 and 1.47 is about 0.4292. 7. **Calculate area left of z = -1.47:** Area left of -1.47 is equal to the area to the right of 1.47. Since total area right of 0 is 0.5, area right of 1.47 = 0.5 - 0.4292 = 0.0708. **Final answers:** - Area between z = -0.67 and z = 0 is **$0.2514$**. - Area to the left of z = -1.47 is **$0.0708$**.