Single scaled time period

Questions that require scaling the Poisson parameter to a single different time period and calculating probabilities for that period only.

2 questions

OCR S2 2010 June Q1
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 \(\operatorname { Po } ( 4.2 )\).
    (a) Find the probability that in the course of a 10-year period, at least 7 inhabitants are selected for jury service.
    (b) Find the probability that in 1 year, exactly 2 inhabitants are selected for jury service.
  2. 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.
Edexcel S2 2010 January Q3
  1. A robot is programmed to build cars on a production line. The robot breaks down at random at a rate of once every 20 hours.
    1. Find the probability that it will work continuously for 5 hours without a breakdown.
    Find the probability that, in an 8 hour period,
  2. the robot will break down at least once,
  3. there are exactly 2 breakdowns. In a particular 8 hour period, the robot broke down twice.
  4. Write down the probability that the robot will break down in the following 8 hour period. Give a reason for your answer.