Mathematics > QUESTION PAPER (QP) > OCR A Level Further Mathematics B (MEI) Y422-01 Statistics Major Friday 17 June 2022 – Afternoon (All)

OCR A Level Further Mathematics B (MEI) Y422-01 Statistics Major Friday 17 June 2022 – Afternoon

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Answer all the questions. Section A (25 marks) 1 During a meteor shower, the number of meteors that can be seen at a particular location can be modelled by a Poisson distribution with mean 1.2 per ... minute. (a) Find the probability that exactly 2 meteors are seen in a period of 1 minute. [1] (b) Find the probability that more than 3 meteors are seen in a period of 1 minute. [2] (c) Find the probability that no more than 8 meteors are seen in a period of 10 minutes. [2] (d) Explain what the fact that the number of meteors seen can be modelled by a Poisson distribution tells you about the occurrence of meteors. [2] 2 A manufacturer is testing how long coloured LED lights will last before the battery runs out, using two different battery types. The times in hours before the battery runs out are modelled by independent Normal distributions with means and standard deviations as shown in the table. Time Type Mean Standard deviation A 23 2.8 B 35 3.6 (a) In a particular test, a battery of type A is used and the time taken for it to run out is recorded. This process is repeated until a total of 5 randomly selected batteries have been used. Determine the probability that the total time the 5 batteries last is at least 120 hours. [3] (b) In a similar test, 3 randomly selected batteries of type A are used, one after the other. Then 2 randomly selected batteries of type B are used, one after the other. Determine the probability that the 3 type A batteries last longer in total than the 2 type B batteries. [3] (c) Explain why it is necessary that the Normal distributions are independent in order to be able to [Show More]

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