Question 1196344
**1. P(Z >= 0)**

* **Understanding z_α:** 
    * z_α represents the z-score that corresponds to the right-tail probability of α in a standard normal distribution. 
    * In other words, P(Z >= z_α) = α

* **Symmetry of Standard Normal Distribution:**
    * The standard normal distribution is symmetric around 0. 
    * Therefore, P(Z >= 0) = 0.5

**2. P(Z <= 5)**

* **Large Z-values:** For very large values of z (like 5), the probability of Z being less than that value is extremely close to 1. 
    * This is because the standard normal distribution extends indefinitely to the right, but with diminishing probability density.

* **In terms of α:** Since P(Z >= z_α) = α represents a right-tail probability, and P(Z <= 5) covers almost the entire distribution, we can approximate:
    * P(Z <= 5) ≈ 1 - α 

**In summary:**

* P(Z >= 0) = 0.5
* P(Z <= 5) ≈ 1 - α