Validity of Poisson model

A question is this type if and only if it asks the student to justify, critique, or explain whether a Poisson distribution is an appropriate model, based on conditions such as independence, constant rate, or comparing mean and variance.

3 questions · Standard +0.1

5.02i Poisson distribution: random events model
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OCR MEI S2 2007 June Q3
16 marks Standard +0.3
3 The number of calls received at an office per 5 minutes is modelled by a Poisson distribution with mean 3.2.
  1. Find the probability of
    (A) exactly one call in a 5 -minute period,
    (B) at least 6 calls in a 5 -minute period.
  2. Find the probability of
    (A) exactly one call in a 1 -minute period,
    (B) exactly one call in each of five successive 1-minute periods.
  3. Use a suitable approximating distribution to find the probability of at most 45 calls in a period of 1 hour. Two assumptions required for a Poisson distribution to be a suitable model are that calls arrive
OCR S2 2010 June Q1
7 marks Moderate -0.3
1
  1. The number of inhabitants of a village who are selected for jury service in the course of a 10-year period is a random variable with the distribution \(\operatorname { Po } ( 4.2 )\).
    1. Find the probability that in the course of a 10-year period, at least 7 inhabitants are selected for jury service.
    2. Find the probability that in 1 year, exactly 2 inhabitants are selected for jury service.
    3. Explain why the number of inhabitants of the village who contract influenza in 1 year can probably not be well modelled by a Poisson distribution.
AQA Further Paper 3 Statistics 2022 June Q4
5 marks Standard +0.3
4 Daisies and dandelions are the only flowers growing in a field. The number of daisies per square metre in the field has a mean of 16
The number of dandelions per square metre in the field has a mean of 10
The number of daisies per square metre and the number of dandelions per square metre are independent. 4
  1. Using a Poisson model, find the probability that a randomly selected square metre from the field has a total of at least 30 flowers, giving your answer to three decimal places.
    4
  2. A survey of the entire field is taken.
    The standard deviation of the total number of flowers per square metre is 10 State, with a reason, whether the model used in part (a) is valid.