Problem N5731 probability theory estimate the true

Problem N5731 probability theory estimate the true

5731. x̅=42.8, n=16, s=8 Based on the data of 16 independent equal-accurate measurements of a certain physical quantity, the arithmetic mean of the measurement results was found equal to x̅в=42.8 and the "corrected" standard deviation s=8. Estimate the true value of the measured value with reliability γ=0.999.

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