| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Approximating the Poisson to the Normal distribution |
| Type | Scaled Poisson over time period |
| Difficulty | Moderate -0.3 This is a straightforward S2 question testing standard Poisson distribution knowledge and normal approximation. Part (a) requires recall of conditions, part (b) is routine Poisson calculation with tables, and part (c) applies the standard normal approximation formula with continuity correction. All steps are textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04d Normal approximation to binomial5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x! |
A botanist suggests that the number of a particular variety of weed growing in a meadow can be modelled by a Poisson distribution.
\begin{enumerate}[label=(\alph*)]
\item Write down two conditions that must apply for this model to be applicable. [2]
\end{enumerate}
Assuming this model and a mean of 0.7 weeds per m², find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the probability that in a randomly chosen plot of size 4 m² there will be fewer than 3 of these weeds, [4]
\item Using a suitable approximation, find the probability that in a plot of 100 m² there will be more than 66 of these weeds. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q3 [12]}}