Solution of problem N219 Laplace probability theory

Solution of problem N219 Laplace probability theory

219. There are 100 machines of the same capacity working independently of each other in the same mode, at which their drive with a probability of 0.8 turns on during the entire working time. What is the probability that at an arbitrarily taken time will turn on from 70 to 86 machines?

Additional information:

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