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Transcription of this question: [Maximum mark: 13]The number of taxis arriving at Cardiff Central railway station can be modelled by a Poissondistribution. During busy periods of the day, taxis arrive at a mean rate of 5.3 taxis every10 minutes. Let T represent a random 10 minute busy period.(ii)(iii)Find the probability that exactly 4 taxis arrive during T.Find the most likely number of taxis that would arrive during T.Given that more than 5 taxis arrive during T , find the probability that exactly7 taxis arrive during T.During quiet periods of the day, taxis arrive at a mean rate of 1.3 taxis every 10 minutes.(b) Find the probability that during a period of 15 minutes, of which the first 10 minutes isbusy and the next 5 minutes is quiet, that exactly 2 taxis arrive.[7][6]

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