Edexcel S2 — Question 2 7 marks

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Marks7
PaperDownload PDF ↗
TopicPoisson distribution
TypeMultiple independent time periods
DifficultyModerate -0.8 This is a straightforward application of the Poisson distribution formula with clearly stated parameters. Part (a) is pure substitution into P(X=0), part (b) requires recognizing the rate scales to λ=5.4 for 6 months, and part (c) combines Poisson with binomial reasoning. All steps are standard textbook exercises with no novel insight required, making this easier than average.
Spec5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities

On a stretch of motorway accidents occur at a rate of 0.9 per month.
  1. Show that the probability of no accidents in the next month is 0.407, to 3 significant figures. [1] Find the probability of
  2. exactly 2 accidents in the next 6 month period, [3]
  3. no accidents in exactly 2 of the next 4 months. [3]

On a stretch of motorway accidents occur at a rate of 0.9 per month.

\begin{enumerate}[label=(\alph*)]
\item Show that the probability of no accidents in the next month is 0.407, to 3 significant figures. [1]

Find the probability of
\item exactly 2 accidents in the next 6 month period, [3]
\item no accidents in exactly 2 of the next 4 months. [3]
\end{enumerate}

\hfill \mbox{\textit{Edexcel S2  Q2 [7]}}