The critical value that corresponds to a 96.3% confidence level, assuming a normally distributed population, is approximately $\pm 2.086$.

Would you like more details on this process or have any further questions?

Here are 8 related questions you might find useful:

1. How do you interpret the critical value in a confidence interval?
2. What happens to the confidence interval if the sample size is increased?
3. How do you calculate the margin of error for a confidence interval?
4. Why is the critical value different for different confidence levels?
5. How would the critical value change for a smaller confidence level, such as 90%?
6. What is the difference between using a z-score and a t-score for confidence intervals?
7. How does the standard error relate to the confidence interval?
8. Can you use the same critical value for non-normal distributions?

Tip: Always ensure the sample size is adequate when estimating a population mean, as small sample sizes can increase variability in the confidence interval.