State condition for normal approximation

A question is this type if and only if it explicitly asks to state the condition under which normal distribution may approximate Poisson distribution (typically λ ≥ 10 or λ large).

2 questions

Edexcel S2 2017 January Q3
3. (a) State the condition under which the normal distribution may be used as an approximation to the Poisson distribution. The number of reported first aid incidents per week at an airport terminal has a Poisson distribution with mean 3.5
(b) Find the modal number of reported first aid incidents in a randomly selected week. Justify your answer. The random variable \(X\) represents the number of reported first aid incidents at this airport terminal in the next 2 weeks.
(c) Find \(\mathrm { P } ( X > 5 )\)
(d) Given that there were exactly 6 reported first aid incidents in a 2 week period, find the probability that exactly 4 were reported in the first week.
(e) Using a suitable approximation, find the probability that in the next 40 weeks there will be at least 120 reported first aid incidents.
Edexcel S2 2003 June Q1
  1. Explain briefly what you understand by
    1. a statistic,
    2. a sampling distribution.
    3. (a) Write down the condition needed to approximate a Poisson distribution by a Normal distribution.
    The random variable \(Y \sim \operatorname { Po } ( 30 )\).
  2. Estimate \(\mathrm { P } ( Y > 28 )\).