Problem N5729 probability theory sample size

Problem N5729 probability theory sample size

5729. Shop workers are being examined. Based on a sample size of n=144, the average monthly output of workers (in units) was found. Find with a reliability of 0.99 the accuracy δ with which the sample mean estimates the mathematical expectation of monthly output, knowing that the monthly output of a worker is normally distributed with a standard deviation σ=10.

Additional information:

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