In the "LPD Poisson Model" the reasonable approximation is made that lead risk is assigned only to properties with lead service pipes. If the lead pipe density is the same for all zones then the two random models (Uniform and LPD) are identical and they would both predict the same zonal compliance distribution. However, as already shown there is wide variation in LPD across zones and this should have substantial implications for the predicted zonal compliance distribution. Calculations found that the chi-squared is reduced from 961 for the Uniform Poisson Model (U) to 553 for the LPD Poisson Model (L) (Table ). It is concluded that variation in LPD accounts for a substantial amount of the nonrandom variation in lead non-compliance across zones. However, the value of chi-squared still indicates there is a substantial non-random component in the distribution. As per previous analysis exact binomial calculations were carried out to see if some of this variation could be accounted for by outliers. Two outlier zones were the same two anomalous cases identified by the Uniform Poisson Model. The other four outliers previously found are no longer outliers indicating that their status as outliers is accounted for by the high proportion of lead pipes in these zones. As previously removing the two anomalous zones further reduces the chi-squared but there remains a significant non-random component (L-X2). Comparison between the observed and theoretical zonal compliance distributions (Figure ) shows that the LPD model captures the major features of the observed distribution much better than the Uniform Poisson Model. The theoretical distribution was calculated for the LPD Poisson Model using the Monte Carlo method. This involved two random binomial calculations. First, the number of properties with lead service pipes in a zone was determined by random selection from a binomial distribution based on the zonal LPD. Then the number of those properties that were at a risk of infringing the standard was determined by randomly sampling from a binomial distribution given the likelihood of infringing the standard amongst properties with lead service pipes. This calculation was carried out for all zones and then repeated 10,000 times. Comparison of Figure with Figure shows that the LPD Poisson Model has significantly improved the zero-inflated aspect of the distribution. The Uniform Poisson Model predicted 18 zones with 100 % compliance compared to the observed 49. The LPD Poisson Model predicted on average 56 zones with no infringements. Though the prediction is notably higher analysis shows that the difference is not statistically significant.