The best point estimate for the population mean, based on the sample, is the sample mean itself.

In this case, the sample mean is $\bar{x} = 512$. Therefore, the best point estimate for the population mean is 512.

Would you like to see how to construct the 99% confidence interval using this information? If so, I can walk you through the steps.

Here are some related questions:

1. What is a confidence interval and why is it important in statistics?
2. How do you calculate the margin of error for a confidence interval?
3. What is the formula for a confidence interval for the population mean when the population standard deviation is unknown?
4. How does the sample size affect the width of a confidence interval?
5. What is the difference between a 95% and a 99% confidence interval?
6. How do you determine the critical value (z-score) for a 99% confidence interval?
7. What assumptions must be met to construct a confidence interval for the mean?
8. How does the standard deviation of the sample influence the confidence interval?

Tip: When estimating a population mean, the larger the sample size, the more precise your confidence interval will be.