A busy junction is a site of frequent car accidents. Data on the number of accidents per month was collected over a period of two years. The table below shows this data. grouped by number of accidents per month. For this question you may assume that a month is exactly four weeks. llnnnnan nnalannn Assume that the number of accidents per month follows a Poisson distribution. {a} Calculate the parameter A of the Poisson distribution describing the number of accidents per month. {2 marks} {b} exactly two accidents in a given month? {2 marks} {c} at least three accidents in a given month? {2 marks} {d} exactly one accident in each of the next three months? {2 marks} {e} no accidents in a year? {3 marks} {t} Use an exponential distribution to find the probability that two accidents are more than three weeks apart. {3 marks} The data is summarised in the chart below. llil I1 I3 II It I? chtaJ {g} Comment on any problems with this chart. and suggest improvements. {4 marks}