Problem N5581 probability theory confidence interval

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5581. x̅=120.20, n=50, σ=2. Find the confidence interval for estimating with a reliability of 0.99 the unknown mathematical expectation a of a normally distributed feature X of the general population, knowing the sample mean x̅=120.20, the sample size n=50, and the standard deviation σ=2.
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)