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Transcription of this question: 12.[Maximum mark: 221A ski resort finds that the mean number Of accidents on any given weekday (Mondayto Friday) is 2.2. The number Of accidents can be modelled by a Poisson distribution.(a) Find the probability that in a certain week (Monday to Friday only)(i) there are fewer than 12 accidents;(ii) there aremore than 8 accidents, given that there are fewer than 12 accidents.Due to the increased usage, it is found that the probability of more than 3 accidents ina day at the weekend (Saturday and Sunday) is 0.24.(b) Assuming a Poisson model,(i) calculate the mean number Of accidents per day at the weekend (Saturdayand Sunday);(ii) calculate the probability that, in the four weekends in February, there willbe more than 5 accidents during at least two Of the weekends.It is found that 20 % of skiers having accidents are at least 25 years of age and 40 %are under 1 8 years Of age.(c) Assuming that the ages Of skiers having accidents are normally distributed,find the mean age Of skiers having accidents.[6 marks][I O marks][6 marks]

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