The numbers of accidents which occur on an assembly line each week over a 2 year period are summarised in Table 1. Table 1: Number of accidents, a Frequency 0 1 1 14 2 21 3 36 4 18 5 9 6 2 7 1 8 2 (a) Use the data to compute the sample mean number of accidents recorded per area. (b) Suppose the data in Table 1 follows a Poisson distribution. Calculate the theoretical Poisson(A = 3) probabilities for integers in the range 0 to 9 inclusive. (c) Does this Poisson distribution provide a good model for the number of accidents in this example (as per Table 1)? Explain why or why not. Use R to produce a graph to help support your answer (produce the R as part of your answer). (d) Use the model in (b) to estimate the probability that less than 2 accidents were recorded in any randomly chosen week. How does this compare to the actual data?