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Transcription of this question: 12.[Maximum mark: 18]The number Of accidents that occur at a large factory can be modelled by a Poissondistribution with a mean Of 0.5 accidents per month.(a)(b)(c)(d)Find the probability that no accidents occur in a given month.Find the probability that no accidents occur in a given 6 month period.Find the length Of time, in complete months, for which the probability that atleast 1 accident occurs is greater than 0.99.TO encourage safety the factory pays a bonus Of S 1000 into a fund for workers ifno accidents occur in any given month, a bonus Of $500 if 1 or 2 accidents occurand no bonus if more than 2 accidents occur in the month.(i)(ii)Calculate the expected amount that the company will pay in bonuseseach month.Find the probability that in a given 3 month period the company pays atotal of exactly in bonuses.[l mark][2 marks][6 marks][9 marks]

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