Problem N5724 probability theory sample size

Problem N5724 probability theory sample size

5724. Automatic machine stamps rollers. Based on a sample of volume n=100, the sample average of the diameters of the manufactured rollers was calculated. Find with a reliability of 0.95 the accuracy δ with which the sample mean estimates the mathematical expectation of the diameters of the manufactured rollers, knowing that their standard deviation σ=2 mm. It is assumed that the diameters of the beads are normally distributed.

Additional information:

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