| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2003 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating the Poisson to the Normal distribution |
| Type | State condition for normal approximation |
| Difficulty | Moderate -0.3 Part (a) is pure recall of a standard condition (λ ≥ 10 or similar). Part (b) requires applying the normal approximation with continuity correction and standardization, which is a routine S2 technique with multiple steps but no novel insight. The 6 marks reflect mechanical application rather than conceptual difficulty. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
\begin{enumerate}[label=(\alph*)]
\item Write down the condition needed to approximate a Poisson distribution by a Normal distribution. [1]
\end{enumerate}
The random variable $Y \sim \text{Po}(30)$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Estimate P($Y > 28$). [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2003 Q2 [7]}}