I am trying to quantify my concerns regarding a proposed incinerator in our community. The company is basing its potential to emit dioxins (a class of chlorinated organic compounds with a reference dose of 1.7E-8 grams per 150 lb person per year) on three emission measurements (mg/m^3 exhaust):
0.0002139; 0.0000014; 0.00000186
The company has submitted their potential to emit as the mean of these three values, which is near legal limits. If the plant is built, they may be required to measure dioxins only once on completion, or possibly every year thereafter.
My initial thoughts have been to find the probability that these samples were drawn from a distribution with a mean above a certain threshold (e.g. the legal limit). As sample measurements, I would assume a normal distribution, though I guess with some non-zero skewness. I don't have any prior knowledge about the variance other than the samples.
But, I am now confronted with an infinite number of possible distributions, and am unsure how to proceed. I suspect this is a well studied area of statistics (risk analysis?), and any pointers in common methods would be much appreciated. I am a biochemist, and statistics is not my first language.