The gross assumption that all properties have the same risk is not critical. If instead it is assumed that lead risk derives from lead service pipes and that only 20% of properties in all zones had lead service pipes then the results in Table and Figure are still applicable provided the sample size is large; this is a consequence of the Poisson nature of the problem. In the case at hand the average number of samples per zone is 239. The assumption that the proportion of properties with lead service pipes is the same in all zones is key to this model. To emphasize this assumption, it will be referred to as the Uniform Poisson Model.