Solution of problem N1417 Laplace probability theory

Solution of problem N1417 Laplace probability theory

1417. In the manufacture of colored tiles, 70% of products are top-notch. How many tiles to take, so that with a probability of more than 0.95, it could be argued that the share of first-class among them differs in absolute value from the probability of no more than 0.05?

Additional information:

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