| Exam Board | CAIE |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2020 |
| Session | Specimen |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single scaled time period |
| Difficulty | Moderate -0.3 This is a straightforward Poisson distribution question requiring only standard calculations: scaling the rate parameter for different time periods and computing probabilities using the formula or tables. Part (a) is direct substitution, part (b) requires P(X≥3)=1-P(X≤2) which is routine. No problem-solving insight needed, just careful arithmetic with a familiar distribution. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x! |
The number of calls received at a small call centre has a Poisson distribution with mean 2 calls per 5 minute period.
\begin{enumerate}[label=(\alph*)]
\item Find the probability exactly 4 calls in a 10 minute period. [2]
\item Find the probability at least 3 calls in a 3 minute period. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE S2 2020 Q3 [5]}}