Problem N5585 probability theory confidence interval

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5585. x̅=114.36, n=81, σ=9. Find the confidence interval for estimating with a reliability of 0.99 the unknown mathematical expectation a of the normal distributed feature X of the general population, knowing the sample mean x̅=114.36, the sample size n=81 and the standard deviation σ=9.
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)