The normal distribution applies to many situations where measurements are subject to random errors. At first it may seem strange that some of the same formulas apply to diffusion and statistics but in diffusion we are concerned with concentrations or particle densities and in statistics with populations and frequencies of events. The expansion that Einstein used to derive Fick's Second Law shows the generality of the results. The similar formulas allow us to use tables of confidence intervals to get results for diffusion but we have remember that instead of standard deviations we are dealing with diffusion lengths that change over time.
Certainly errors were made in the Gulf of Mexico and it is likely that there are still lessons to be learned. Both the oil industry and the government need to review what happened and see what can be done to avoid making the same mistakes in the future.