Calculate the probability for the following problems (Please keep 4 decimal places). 1. \( P(z>-0.7)= \) 2. \( P(z<2.39)= \) 3. \( P(-0.8

Ask by Hamilton Spencer. in the United States

Mar 17,2025

To calculate the probabilities associated with a standard normal distribution (Z-distribution), we'll use the Z-table or standard normal distribution properties. 1. For \( P(z > -0.7) \), we first find \( P(z < -0.7) \) using the Z-table, which gives us approximately 0.2420. Since the total probability is 1, we can find \( P(z > -0.7) \) by subtracting: \( P(z > -0.7) = 1 - P(z < -0.7) = 1 - 0.2420 = 0.7580 \). 2. For \( P(z < 2.39) \), we can directly look it up in the Z-table, which typically gives us around 0.9918. Thus: \( P(z < 2.39) = 0.9918 \). 3. For \( P(-0.8 < z < 0.08) \), we compute it as: \( P(z < 0.08) - P(z < -0.8) \). From the Z-table, \( P(z < 0.08) \approx 0.5319 \) and \( P(z < -0.8) \approx 0.2119 \). Therefore: \( P(-0.8 < z < 0.08) = 0.5319 - 0.2119 = 0.3200 \). So the answers are: 1. \( P(z > -0.7) = 0.7580 \) 2. \( P(z < 2.39) = 0.9918 \) 3. \( P(-0.8 < z < 0.08) = 0.3200 \)