CAIE S2 2020 Specimen — Question 3 5 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2020
SessionSpecimen
Marks5
PaperDownload PDF ↗
TopicPoisson distribution
TypeSingle scaled time period
DifficultyModerate -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.
Spec5.02i 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.
  1. Find the probability exactly 4 calls in a 10 minute period. [2]
  2. Find the probability at least 3 calls in a 3 minute period. [3]

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]}}