1. **State the problem:** Diane's home price is $737000. The mean home price in the area is $785000 with a standard deviation of $18050. We need to find the z-score of Diane's home price relative to the area prices. 2. **Formula for z-score:** $$z = \frac{X - \mu}{\sigma}$$ where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. 3. **Substitute the values:** $$z = \frac{737000 - 785000}{18050}$$ 4. **Calculate the numerator:** $$737000 - 785000 = -48000$$ 5. **Calculate the z-score:** $$z = \frac{-48000}{18050} \approx -2.66$$ 6. **Interpretation:** The z-score of -2.66 means Diane's home price is 2.66 standard deviations below the mean home price in the area. **Final answer:** $$z \approx -2.66$$