On the average five accidents per 10, 000 passing vehicles have been observed on a particular piece of road. What is the probability that, in the next interval of 10, 000 passages, between two and eight accidents will be observed? (Assume that the number of trials-possible accident situations-is sufficiently large that a Poisson approximation is valid.) Suppose a new side road entering on this road has been added and it is desired to study its influence on safety: that is, has the average accident rate increased since this road was added? This question will be studied by observing the number of accidents in the next interval of 10, 000 cars. The problem is that that number is random, and even if there has been no degradation of safety (i.e., no increase in average accident rate), there is a small probability that a large number of accidents will occur in the next interval. Suppose in this case nine accidents were observed in the 10, 000 car interval after the side-road installation. Has the average rate increased or was this just a rare occurrence of a large number of accidents with the unchanged average rate of 5? In practice this question is often answered by saying, "If the observation represents a ‘quite rare' event (say with probability of occurrence less than 5 percent) for an unchanged average rate, then ‘probably' the rate is not unchanged but increased." Is the probability of nine or more accidents with an unchanged average rate 5, small enough."