Find the indicated probability using the standard normal distribution. \( P(-0.93

Ask by Riley Franklin. in the United States

Feb 18,2025

To find the probability \( P(-0.93 < z < 0) \) using the standard normal distribution, we can follow these steps: 1. **Find the cumulative probability for \( z = 0 \)**: The cumulative probability for \( z = 0 \) in the standard normal distribution is 0.5, since the mean of the standard normal distribution is 0. 2. **Find the cumulative probability for \( z = -0.93 \)**: We will look up the value of \( P(z < -0.93) \) in the standard normal table. 3. **Calculate the probability**: The probability \( P(-0.93 < z < 0) \) can be calculated as: \[ P(-0.93 < z < 0) = P(z < 0) - P(z < -0.93) \] Now, let's find \( P(z < -0.93) \) using the standard normal table. Looking up \( z = -0.93 \) in the standard normal table, we find that: \[ P(z < -0.93) \approx 0.1762 \] Now we can calculate the probability: \[ P(-0.93 < z < 0) = P(z < 0) - P(z < -0.93) = 0.5 - 0.1762 \] Calculating this gives: \[ P(-0.93 < z < 0) = 0.5 - 0.1762 = 0.3238 \] Thus, the final answer is: \[ P(-0.93 < z < 0) \approx 0.3238 \] So, rounding to four decimal places, we have: \[ P(-0.93 < z < 0) = 0.3238 \]