1. **Problem:** Find the probability $P(-1.6 \leq z \leq 0.8)$ for a standard normal distribution. 2. **Formula and rules:** For a standard normal distribution, probabilities correspond to areas under the curve. Use the cumulative distribution function (CDF) $\Phi(z)$ to find probabilities: $$P(a \leq z \leq b) = \Phi(b) - \Phi(a)$$ where $\Phi(z)$ is the probability that $Z$ is less than or equal to $z$. 3. **Find $\Phi(0.8)$ and $\Phi(-1.6)$:** From standard normal tables or a calculator: $$\Phi(0.8) \approx 0.7881$$ $$\Phi(-1.6) \approx 0.0550$$ 4. **Calculate the probability:** $$P(-1.6 \leq z \leq 0.8) = \Phi(0.8) - \Phi(-1.6) = 0.7881 - 0.0550 = 0.7331$$ 5. **Interpretation:** There is approximately a 73.31% chance that the z-score lies between -1.6 and 0.8. **Final answer:** $$\boxed{0.7331}$$