514. Twelve measurements of a certain physical quantity were made using one instrument (without systematic error), and the "corrected" mean square deviation $s$ of the random errors of the measurements turned out to be 0.6. Find the accuracy of the instrument with a reliability of 0.99. It is assumed that the measurement results are normally distributed.
Solution. The accuracy of the instrument is characterized by the root mean square deviation of random measurement errors. Therefore, the problem reduces to finding a confidence interval that covers $\sigma$ with a given confidence level $\gamma=0.99$:

$$
s(1-q)<\sigma<s(1+q)
$$

Given $\gamma=0.99$ and $n=12$, we find $q=0.9$ from the table in Appendix 4. Substituting $s=0.6, q=0.9$ into the relation (*), we finally get $0.06<\sigma<1.14$.