1. **Problem:** Find the probability $P(-0.73 < Z < 0.63)$ where $Z$ is a standard normal variable. 2. **Formula and rules:** For a standard normal distribution, probabilities between two $Z$-scores are found by subtracting their cumulative distribution function (CDF) values: $$P(a < Z < b) = \Phi(b) - \Phi(a)$$ where $\Phi(z)$ is the CDF of the standard normal distribution. 3. **Find $\Phi(-0.73)$ and $\Phi(0.63)$:** Using standard normal tables or a calculator: $$\Phi(-0.73) \approx 0.2327$$ $$\Phi(0.63) \approx 0.7357$$ 4. **Calculate the probability:** $$P(-0.73 < Z < 0.63) = 0.7357 - 0.2327 = 0.5030$$ 5. **Interpretation:** This means there is approximately a 50.3% chance that the standard normal variable $Z$ falls between -0.73 and 0.63. **Final answer:** $$\boxed{0.5030}$$