I am looking at a packaging operation. I recently did some random sampling and counted how many pieces of a specific part were in each bag. I looked at 101 bags. The number of parts in each bag ranged from 0 to 5 pieces and a mean of 2.33 pieces. If there are 0 parts in a bag, then my company would consider the part as failed.
Here's the question. If I found only 1 bag with 0 parts, do I consider the probability of finding a failed part as (1/101) or do I use the poisson distribution with a mean of 2.33 and calculate the probability of finding 0 pieces that way?