Problem N5584 probability theory confidence interval

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5584. x̅=122.52, n=196, σ=0.7. 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=122.52, the sample size n=196 and the standard deviation σ=0.7.
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)