2. [24 marks] a) A photocopier company kept records of the number of breakdowns per year for 100 photocopiers, giving the results Number of breakdowns 0 1 2 3 24 Frequency 8 20 37 24 11 Test at the 5% level that the above data comes from a Poisson (1 = 2) distribution. b) Two companies manufacture white board pens. A sample of 10 pens from one company and 8 pens from the other were tested until they were no longer readable. The results (in hours) were: Company 1 8.9 9.9 12 7.4 6.6 8.4 7.6 10.9 11.7 10.2 Company 2 9.1 13.3 8.2 11.1 10 11.6 10.5 8.7 Using the Wilcoxon Test for large samples, test at the 5% level the hy- pothesis that there is no difference between the two company's pens