Problem N5630 probability theory confidence interval

Problem N5630 probability theory confidence interval

5630. The arithmetic mean length of the part, equal to x̅v=50 mm, was found from a large batch of manufactured parts using a sample of volume n=64. Assuming that the length of the part X is a normally distributed random variable, find the confidence interval that, with reliability γ=0.95, covers the unknown mathematical expectation of the length of the part if the general standard deviation σ=0.5 mm

Additional information:

Detailed solution. Decorated in Microsoft Word 2003 (Quest decided to use the formula editor)