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)?

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