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

To calculate these probabilities, we will use the standard normal distribution table (Z-table), which provides the area under the curve up to a given z-value. 1. For \( P(z > -0.48) \): - First, we find \( P(z < -0.48) \) from the Z-table. The table gives us approximately \( 0.3186 \) for \( -0.48 \). - Therefore, \( P(z > -0.48) = 1 - P(z < -0.48) = 1 - 0.3186 = 0.6814 \). 2. For \( P(z < 0.7) \): - Using the Z-table, we find \( P(z < 0.7) \) which is approximately \( 0.7580 \). 3. For \( P(-0.61 < z < 2.27) \): - First, we find \( P(z < 2.27) \) from the Z-table, which is approximately \( 0.9887 \). - Then, we find \( P(z < -0.61) \), which is approximately \( 0.2709 \). - Therefore, \( P(-0.61 < z < 2.27) = P(z < 2.27) - P(z < -0.61) = 0.9887 - 0.2709 = 0.7178 \). Putting it all together, the probabilities are: 1. \( P(z > -0.48) = 0.6814 \) 2. \( P(z < 0.7) = 0.7580 \) 3. \( P(-0.61 < z < 2.27) = 0.7178 \)