1. The problem states that for a standard normal distribution $Z$, we want to find the value $z^*$ such that $P(Z \geq z^*) = 0.025$. 2. Since the total area under the normal curve is 1, the area to the left of $z^*$ is $1 - 0.025 = 0.975$. 3. We need to find the $z^*$ value corresponding to the cumulative probability $0.975$ in the standard normal distribution. 4. Using standard normal distribution tables or a calculator, the $z$-score for $P(Z \leq z^*) = 0.975$ is approximately $z^* = 1.96$. 5. Therefore, the value $z^*$ such that $P(Z \geq z^*) = 0.025$ is $\boxed{1.96}$. This means that 2.5% of the distribution lies to the right of $z^* = 1.96$ on the standard normal curve.