510. According to the data of nine independent equi-precise measurements of a certain physical quantity, the arithmetic mean of the measurement results $\bar{x}_{\mathrm{v}}=30.1$ and the corrected mean square deviation $s=6$ have been found. Estimate the true value of the measured quantity using a confidence interval with reliability $\gamma=0.99$. It is assumed that the measurement results are normally distributed.
Solution. The true value of the measured quantity is equal to its mathematical expectation a. Therefore, the problem reduces to estimating the mathematical expectation (with an unknown b) using a confidence interval

$$
\bar{x}_{B}-t_{\gamma} s / \sqrt{n}<a<\bar{x}_{B}+t_{\gamma} s / \sqrt{n}
$$

All quantities except $t_{\gamma}$ are known. Let's find $t_{\gamma}$. From the table in Appendix 3, for $\gamma=0.99$ and $n=9$, we find $t_{\gamma}=2.36$.

Substituting $\bar{x}_{\mathrm{B}}=30.1, t_{\gamma}=2.36, s=6, n=9$ into (*), we obtain the desired interval: $25.38<a<34.82$.