1. **Problem Statement:** Find the probability that a randomly selected gas tank holds at least 16.5 gallons, given the tank capacity is normally distributed with mean $\mu=14$ gallons and standard deviation $\sigma=15$ gallons. 2. **Formula Used:** For a normal distribution, the probability that $X$ is greater than a value $a$ is given by $$P(X > a) = 1 - P(Z \leq z)$$ where $Z = \frac{X - \mu}{\sigma}$ is the standard normal variable. 3. **Calculate the Z-score:** $$z = \frac{16.5 - 14}{15} = \frac{2.5}{15} = 0.1667$$ 4. **Find the cumulative probability for $z=0.1667$:** Using standard normal tables or a calculator, $$P(Z \leq 0.1667) \approx 0.5662$$ 5. **Calculate the required probability:** $$P(X \geq 16.5) = 1 - 0.5662 = 0.4338$$ 6. **Interpretation:** There is approximately a 43.38% chance that a randomly selected tank will hold at least 16.5 gallons. **Final answer:** $$\boxed{P(X \geq 16.5) \approx 0.4338}$$