1. **State the problem:** We want to find the proportion of Djokovic's first serves with speeds between 120 mph and 130 mph, given that the speeds are normally distributed with mean $\mu=115$ mph and standard deviation $\sigma=6$ mph. 2. **Standardize the values:** Convert the speeds 120 mph and 130 mph to their corresponding $z$-scores using the formula: $$z = \frac{x - \mu}{\sigma}$$ Calculate: $$z_{120} = \frac{120 - 115}{6} = \frac{5}{6} \approx 0.8333$$ $$z_{130} = \frac{130 - 115}{6} = \frac{15}{6} = 2.5$$ 3. **Find the cumulative probabilities:** Use the standard normal distribution table or a calculator to find the cumulative probabilities for these $z$-scores: $$P(Z \leq 0.8333) \approx 0.7977$$ $$P(Z \leq 2.5) \approx 0.9938$$ 4. **Calculate the proportion between 120 and 130 mph:** $$P(120 \leq X \leq 130) = P(Z \leq 2.5) - P(Z \leq 0.8333) = 0.9938 - 0.7977 = 0.1961$$ 5. **Final answer:** Approximately **0.1961** or 19.61% of Djokovic's first serves are between 120 mph and 130 mph.