Problem N5414 probability theory confidence interval

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5414. x̅=18.71, n=25, σ=10. The standard deviation σ=10 of a normally distributed random variable X, sample mean x̅=18.71, sample size n=25 are given. Find confidence intervals for estimating the unknown mathematical expectation a with a given reliability γ=0.95.
Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)