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 variable $Z$, the probability between two values $a$ and $b$ is given by: $$P(a < Z < b) = \Phi(b) - \Phi(a)$$ where $\Phi(x)$ is the cumulative distribution function (CDF) of the standard normal distribution. 3. **Find $\Phi(0.63)$ and $\Phi(-0.73)$:** Using standard normal tables or a calculator: $$\Phi(0.63) \approx 0.7357$$ $$\Phi(-0.73) = 1 - \Phi(0.73) \approx 1 - 0.7673 = 0.2327$$ 4. **Calculate the probability:** $$P(-0.73 < Z < 0.63) = 0.7357 - 0.2327 = 0.5030$$ 5. **Interpretation:** There is approximately a 50.3% chance that the standard normal variable $Z$ lies between -0.73 and 0.63. **Final answer:** $$\boxed{0.5030}$$