1. Stating the problem: Find areas under the standard normal curve for various z-values, specifically areas above or below certain z-scores or between regions. 2. Area above z = 1.46: The area to the right of z = 1.46 is found by $1 - P(Z \leq 1.46)$. Looking up $P(Z \leq 1.46)$ (the cumulative distribution function for z = 1.46), we find approximately 0.9279. So, area above is $$1 - 0.9279 = 0.0721.$$ 3. Area below z = -0.58: The area to the left of z = -0.58 is simply $P(Z \leq -0.58)$. Looking up $P(Z \leq -0.58)$, we get approximately 0.2810. 4. Area greater than z = -1.32: This is the area to the right of z = -1.32, calculated by $$1 - P(Z \leq -1.32).$$ Lookup gives $P(Z \leq -1.32) \approx 0.0934$. So, area is $$1 - 0.0934 = 0.9066.$$ 5. Area at least z = 1 (which means greater than or equal to 1): This area is the same as area above z = 1: $$1 - P(Z \leq 1) = 1 - 0.8413 = 0.1587.$$ Final answers: - Area above z = 1.46: 0.0721 - Area below z = -0.58: 0.2810 - Area greater than z = -1.32: 0.9066 - Area at least z = 1: 0.1587 These values reflect proportions of the total area under the standard normal curve based on z-scores.