Problem N5527 probability theory confidence interval

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5527. x̅=72.18, n=81, σ=6. Find confidence intervals for estimating the mathematical expectation a of a normal distribution with a reliability of 0.95, knowing the sample mean x̅=72.18, the sample size n=81, and the standard deviation σ=6.
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)