Problem N5732 probability theory estimate the true

Problem N5732 probability theory estimate the true

5732. x̅=42.319, n=9, s=5.0 According to 9 independent equal-precision measurements of a physical quantity, the arithmetic mean of the results of individual measurements x̅в=42.319 and the "corrected" standard deviation s=5.0 were found. It is required to estimate the true value a of the measured quantity with the reliability γ=0.99.

Additional information:

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)