Solution of problem N1418 Laplace probability theory

Solution of problem N1418 Laplace probability theory

1418. In the manufacture of facing tiles 70% of products are top-notch. How many tiles should be taken so that with a probability exceeding 0.99, it could be argued that the share of first-class tiles among them will differ from the probability of 0.7 by no more than 0.05 (in absolute value)?

Additional information:

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