1. **Problem:** Find the shaded area under the standard normal distribution curve for the following cases: 2. **Formula and rules:** The standard normal distribution uses the z-score table or cumulative distribution function (CDF) \( \Phi(z) \) to find areas. - Area to the left of \( z \) is \( \Phi(z) \). - Area to the right of \( z \) is \( 1 - \Phi(z) \). - Area between two z-values \( z_1 \) and \( z_2 \) is \( \Phi(z_2) - \Phi(z_1) \). 3. **Calculations:** **(a) Above \( z = 1.46 \):** - Find \( \Phi(1.46) \) from z-table or calculator: approximately 0.9279. - Area above is \( 1 - 0.9279 = 0.0721 \). **(b) Between \( z = 0.76 \) and \( z = 2.88 \):** - \( \Phi(0.76) \approx 0.7764 \) - \( \Phi(2.88) \approx 0.9980 \) - Area between is \( 0.9980 - 0.7764 = 0.2216 \). **(c) To the left of \( z = 2.78 \):** - \( \Phi(2.78) \approx 0.9973 \) - Area to the left is \( 0.9973 \). 4. **Summary:** - Area above \( z=1.46 \) is **0.0721**. - Area between \( z=0.76 \) and \( z=2.88 \) is **0.2216**. - Area to the left of \( z=2.78 \) is **0.9973**. These areas represent probabilities under the normal curve for the given z-values.