Solution of problem N1376 Laplace probability theory

Solution of problem N1376 Laplace probability theory

1376. A new weapon is being tested. The main indicator is the frequency of hits on the standard target for a given set of conditions. The developers claim that the probability of hitting each shot is 0.8. How many shots per target should be made so that with a probability of 0.95 it could be argued that the hit frequency will deviate from the probability of hitting each shot by no more than 0.01 (in absolute value)?

Additional information:

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