Single period normal approximation - scaled period (normal approximation only)

Questions where the rate is scaled up to a longer period and the question asks only for the normal approximation probability, without requiring exact Poisson calculations for a sub-period.

27 questions · Moderate -0.2

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Pre-U Pre-U 9795/2 2013 November Q3
Standard +0.3
3 The number of signal failures in a certain region of the railway network averages 10 every 3 weeks. Assume that signal failures occur independently, randomly and at constant mean rate.
  1. Find the probability that
    1. there are between 7 and 12 (inclusive) signal failures in a three-week period,
    2. there are more than 4 signal failures in a one-week period.
    3. It has been calculated, using a suitable distributional approximation, that the probability of more than 62 signal failures in a period of \(n\) weeks is 0.0385 . Find the value of \(n\).
Edexcel S2 Q5
13 marks Moderate -0.3
A charity receives donations of more than £10000 at an average rate of 25 per year. Find the probability that the charity receives
  1. exactly 30 such donations in one year, [3]
  2. less than 3 such donations in one month. [5]
  3. Using a suitable approximation, find the probability that the charity receives more than 45 donations of more than £10000 in the next two years. [5]