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Standard Normal Probs

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Standard Normal Probs


1. The problem asks to find probabilities related to the standard normal variable $z$. 2. For $P(z < -0.73)$, we look up the cumulative probability for $z = -0.73$ in the standard normal table or use a calculator. 3. Using the standard normal table, $P(z < -0.73) \approx 0.2327$. 4. For $P(z > 2.92)$, we find the cumulative probability for $z = 2.92$ and subtract it from 1. 5. From the table, $P(z < 2.92) \approx 0.9982$, so $P(z > 2.92) = 1 - 0.9982 = 0.0018$. 6. For $P(-3.10 < z < 1.90)$, we find $P(z < 1.90)$ and subtract $P(z < -3.10)$. 7. From the table, $P(z < 1.90) \approx 0.9713$ and $P(z < -3.10) \approx 0.0010$. 8. Therefore, $P(-3.10 < z < 1.90) = 0.9713 - 0.0010 = 0.9703$. Final answers: - $P(z < -0.73) \approx 0.2327$ - $P(z > 2.92) \approx 0.0018$ - $P(-3.10 < z < 1.90) \approx 0.9703$