1. The problem asks to find the critical values $Z_{0.01}$, $Z_{0.05}$, $Z_{0.005}$, and $Z_{0.025}$ from the standard normal distribution. 2. These values correspond to the z-scores where the area to the right under the standard normal curve is equal to the given probabilities: 0.01, 0.05, 0.005, and 0.025 respectively. 3. The formula to find $Z_p$ is to find the z-score such that $P(Z > Z_p) = p$ where $Z$ is a standard normal variable. 4. Using standard normal distribution tables or a calculator, we find: - $Z_{0.01}$ is the z-score with 1% in the right tail, which is approximately $2.33$. - $Z_{0.05}$ is the z-score with 5% in the right tail, approximately $1.645$. - $Z_{0.005}$ is the z-score with 0.5% in the right tail, approximately $2.575$. - $Z_{0.025}$ is the z-score with 2.5% in the right tail, approximately $1.96$. 5. These values are commonly used in hypothesis testing and confidence intervals. Final answers: $$Z_{0.01} = 2.33$$ $$Z_{0.05} = 1.645$$ $$Z_{0.005} = 2.575$$ $$Z_{0.025} = 1.96$$