20.1 Mathematical statistics

Problem: As a result of 10 independent measurements of a certain value \( X \), taken with the same accuracy, the experimental data, shown in the table, were obtained. Assuming that the results of the measurements are subject to a normal probability distribution rule, estimate the true values of \( X \) making use of the confidence interval, covering the true values of \( X \) with a confidence possibility of 0,95 . \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|} \hline\( x_{1} \) & \( x_{2} \) & \( x_{3} \) & \( x_{4} \) & \( x_{5} \) & \( x_{6} \) & \( x_{7} \) & \( x_{8} \) & \( x_{9} \) & \( x_{10} \) \\ \hline 5,3 & 3,7 & 6,2 & 3,9 & 4,4 & 4,9 & 5,0 & 4,1 & 3,8 & 4,2 \\ \hline \end{tabular}