| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2003 |
| Session | January |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single period normal approximation - scaled period (normal approximation only) |
| Difficulty | Easy -1.2 Part (a) is pure recall of standard Poisson conditions with no problem-solving. Parts (b) and (c) are routine applications: scaling the parameter and using a standard normal approximation. This is a straightforward textbook exercise testing basic knowledge and standard procedures. |
| Spec | 2.04d Normal approximation to binomial5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
3. 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.
Assuming this model and a mean of 0.7 weeds per $\mathrm { m } ^ { 2 }$, find
\item the probability that in a randomly chosen plot of size $4 \mathrm {~m} ^ { 2 }$ there will be fewer than 3 of these weeds.
\item Using a suitable approximation, find the probability that in a plot of $100 \mathrm {~m} ^ { 2 }$ there will be more than 66 of these weeds.\\
(6)
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2003 Q3 [12]}}