Suppose that the number of accidents occurring in an industrial plant is described by a Poisson distribution with an average of one accident per month. Let x denote the time ( in months) between successive accidents. a Find the probability that the time between successive accidents is ( 1) More than two months. ( 2) Between one and two months. ( 3) Less than one week ( 1 4 of a month).b Suppose that an accident occurs less than one week after the plant’s most recent accident. Would you consider this event unusual enough to warrant special investigation? Explain.