1. **Problem Statement:** Find the area under the standard normal curve to the left of the given Z-values: a. $Z = -2.48$, b. $Z = 3.00$, c. $Z = 2.42$, d. $Z = 0.99$. 2. **Formula and Explanation:** The area to the left of a Z-value on the standard normal curve corresponds to the cumulative distribution function (CDF) value $\Phi(z)$. 3. **Important Rules:** - The standard normal distribution has mean 0 and standard deviation 1. - The total area under the curve is 1. - For negative Z-values, the area to the left is less than 0.5. - For positive Z-values, the area to the left is greater than 0.5. 4. **Calculations:** - a. For $Z = -2.48$, using standard normal tables or a calculator, $\Phi(-2.48) \approx 0.0066$. - b. For $Z = 3.00$, $\Phi(3.00) \approx 0.9987$. - c. For $Z = 2.42$, $\Phi(2.42) \approx 0.9922$. - d. For $Z = 0.99$, $\Phi(0.99) \approx 0.8389$. 5. **Final Answers:** - a. Area to the left of $Z = -2.48$ is approximately $0.0066$. - b. Area to the left of $Z = 3.00$ is approximately $0.9987$. - c. Area to the left of $Z = 2.42$ is approximately $0.9922$. - d. Area to the left of $Z = 0.99$ is approximately $0.8389$. These values represent the probabilities that a standard normal random variable is less than the given Z-values.