Step 1 :The problem is asking for a 95% confidence interval for the mean level of radon exposure in tombs in the region.
Step 2 :The confidence interval can be calculated using the formula for a confidence interval for a mean, which is \(\bar{x} \pm z \frac{s}{\sqrt{n}}\), where \(\bar{x}\) is the sample mean, \(s\) is the sample standard deviation, \(n\) is the sample size, and \(z\) is the z-score corresponding to the desired level of confidence.
Step 3 :In this case, \(\bar{x} = 3560 \, Bq/m^3\), \(s = 1300 \, Bq/m^3\), \(n = 12\), and the z-score for a 95% confidence interval is approximately 1.96.
Step 4 :Substituting these values into the formula gives a lower bound of 2824 and an upper bound of 4296 for the confidence interval.
Step 5 :Final Answer: The 95% confidence interval for the true mean level of radon exposure in tombs in the region is \(\boxed{2824}, \boxed{4296}\) Bq/m³.
Step 6 :This means that we are 95% confident that the true mean level of radon exposure in tombs in the region lies between 2824 Bq/m³ and 4296 Bq/m³.