5609. From a large batch of electric lamps, 100 were randomly selected. The average duration of lamp burning in the sample turned out to be 1000 hours. Find with reliability γ = 0.95 a confidence interval for the average duration a of lamp burning in the entire batch, if it is known that the standard deviation of the duration lamp burning σ=40 h and the duration of lamp burning is distributed according to the normal law.

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