Problem N5529 probability theory confidence interval

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5529. x̅=85.15, n=49, σ=6. Find confidence intervals for estimating the mathematical expectation, normal distribution with a reliability of 0.95; knowing the sample mean x̅=85.15, the sample size n=49 and the standard deviation σ=6.
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)