Problem N5586 probability theory confidence interval

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5586. x̅=115.52, n=100, σ=10. Find the confidence interval for estimating with a reliability of 0.99 the unknown mathematical expectation a of a normal distributed feature X of the general population, knowing the sample mean x̅=115.52, the sample size n=100 and the standard deviation σ=10.
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)