1189. At stamping 70% of the details come out first grade, 20% - the second and 10% - the third. Determine how many parts to take, so that with a probability of 0.997, it could be argued that the share of first-grade will differ from the probability of manufacturing first-class details by no more than 0.05 (in either direction). Answer the same question if the percentage of first-grade details is unknown.

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