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:
- $P(z < -0.73) \approx 0.2327$
- $P(z > 2.92) \approx 0.0018$
- $P(-3.10 < z < 1.90) \approx 0.9703$