This is a well known problem in microbiology. The standard method is the Most Probable Number (MPN) methods. If you consult the standard reference manuals on quality control for food inspection, you will find the necessary tables for sample size, estimation, confidence levels etc.

The problem is often faced by food inspector who need to determine if the bacterial levels of, e.g. shellfish, are below hazardous levels.

Also, if you do a literature search on MPN in the Current Index to Statistics and many references also occur.

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