Calculate the probability for the following problems (Please keep 4 decimal places). 1. \( P(z>-0.48)=\square \) 2. \( P(z<0.7)=\square \) 3. \( P(-0.61

Ask by Pope Reeves. in the United States

Mar 14,2025

1. To find \( P(z > -0.48) \), use the complement rule: \[ P(z > -0.48) = 1 - P(z \le -0.48) \] From the standard normal table, we have: \[ P(z \le -0.48) \approx 0.3156 \] Thus, \[ P(z > -0.48) \approx 1 - 0.3156 = 0.6844 \] 2. For \( P(z < 0.7) \), look up the cumulative probability for \( z = 0.7 \): \[ P(z < 0.7) \approx 0.7580 \] 3. To calculate \( P(-0.61 < z < 2.27) \), subtract the cumulative probability at \( z = -0.61 \) from the cumulative probability at \( z = 2.27 \): \[ P(-0.61 < z < 2.27) = P(z < 2.27) - P(z \le -0.61) \] From the standard normal table: \[ P(z < 2.27) \approx 0.9884 \quad \text{and} \quad P(z \le -0.61) \approx 0.2709 \] Therefore, \[ P(-0.61 < z < 2.27) \approx 0.9884 - 0.2709 = 0.7175 \] Final Answers (rounded to 4 decimal places): 1. \( P(z > -0.48) \approx 0.6844 \) 2. \( P(z < 0.7) \approx 0.7580 \) 3. \( P(-0.61 < z < 2.27) \approx 0.7175 \)