AQA Further Paper 3 Statistics 2019 June — Question 8

Exam BoardAQA
ModuleFurther Paper 3 Statistics (Further Paper 3 Statistics)
Year2019
SessionJune
TopicPoisson Distribution
TypeMultiple independent time periods

8 The number of telephone calls received by an office can be modelled by a Poisson distribution with mean 3 calls per 10 minutes. 8
  1. Find the probability that:
    8
    1. the office receives exactly 2 calls in 10 minutes; 8
  2. (ii) the office receives more than 30 calls in an hour.
    8
  3. The office manager splits an hour into 6 periods of 10 minutes and records the number of telephone calls received in each of the 10 minute periods. Find the probability that the office receives exactly 2 calls in a 10 minute period exactly twice within an hour.
    8
  4. The office has just received a call.
    8
    1. Find the probability that the next call is received more than 10 minutes later.
      8
  5. (ii) Mahah arrives at the office 5 minutes after the last call was received.
    State the probability that the next call received by the office is received more than 10 minutes later. Explain your answer.
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