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1.15 The data shown in the table below is a four-year record of the number of recordable safety incidents occurring at a plant site each month1 0 0 0 2 2 0 0 01 0 1 0 1 0 1 0 0 0 0 0 0 0 1 2 2 0 1 2 0 1 21 1 0 0 0 1 0 0 0 0 0 0 1 0 0 0 (i) Find the average number of safety incidents per month and the associated vari- ance. Construct a frequency table of the data and plot a histogram (ii) From the frequency table and the histogram, what can you say about the chances of obtaining each of the following observations, where x represents the number of observed safety incidents per month: x = 0,x 1,x = 2,x-3, x = 4 and 5! (iii) Consider the postulate that a reasonable model for this phenomenon is -0.5 0.5 where f(x) represents the theoretical probability of recording exactly r safety incidents per month. How well does this model fit the data? (iv) Assuming that this is a reasonable model, discuss how you would use it to answer the question: If, over the most recent four-month period, the plant recorded 1, 3, 2, 3 safety incidents respectively, is there evidence that there has been a real increase in the number of safety incidents?

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