In many cities, neighborhood Crime Watch groups are formed in an attempt to reduce the amount of criminal activity. Suppose one neighborhood that has experienced an average of 10 crimes per year organizes such a group. During the first year following the creation of the group, 3 crimes are committed in the neighborhood.
a. Use the Poisson distribution to calculate the probability that 3 or fewer crimes are committed in a year, assuming that the average number is still 10 crimes per year.
b. Do you think this event provides some evidence that the Crime Watch group has been effective in this neighborhood?