1. **State the problem:** We want to estimate the population mean number of days it takes to sell a Chevrolet Aveo based on the sample data. We have a sample mean $\bar{x} = 54$ days, population standard deviation $\sigma = 6$, and sample size $n = 50$. We aim to find the best point estimate and the 95% confidence interval for the population mean $\mu$. 2. **Best point estimate:** The sample mean $\bar{x}$ is the best point estimate of the population mean $\mu$. Thus, the best point estimate is $$\hat{\mu} = 54$$ 3. **Find the 95% confidence interval:** Since the population standard deviation $\sigma$ is known, we use the z-distribution. For a 95% confidence level, the critical value $z_{\alpha/2} = 1.96$. 4. **Calculate the standard error:** $$SE = \frac{\sigma}{\sqrt{n}} = \frac{6}{\sqrt{50}} = \frac{6}{7.071} \approx 0.8485$$ 5. **Calculate the margin of error:** $$ME = z_{\alpha/2} \times SE = 1.96 \times 0.8485 \approx 1.663$$ 6. **Construct the confidence interval:** $$CI = \left( \bar{x} - ME, \bar{x} + ME \right) = (54 - 1.663, 54 + 1.663) = (52.337, 55.663)$$ 7. **Conclusion:** We are 95% confident that the true population mean number of days it takes to sell a Chevrolet Aveo is between **52.337** and **55.663** days. **Final answers:** - Best point estimate: $54$ - 95% confidence interval: $\left(52.337, 55.663\right)$