1. The archaeologist has found that vases made by the workshop with a mass less than 1.93 kg are particularly fragile and require special care.

 A museum has just purchased a collection of $k$ vases produced by the workshop.  The $k$ vases may be assumed to be a random sample.

Given that there is a less than 15% chance that the collection contains vases that are particularly fragile and require special care, find the greatest possible value of $k$. Your answer should be supported by clear algebraic working.