| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single period normal approximation - large lambda direct |
| Difficulty | Moderate -0.3 This is a straightforward application of standard Poisson distribution techniques from S2. Parts (a)-(c) involve basic recall of Poisson properties and direct calculator/formula work. Part (d) requires a normal approximation with continuity correction, which is a standard bookwork procedure. The question is slightly easier than average because it's highly structured with clear signposting and no conceptual surprises—students simply follow learned 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! |
An Internet service provider has a large number of users regularly connecting to its computers. On average only 3 users every hour fail to connect to the Internet at their first attempt.
\begin{enumerate}[label=(\alph*)]
\item Give 2 reasons why a Poisson distribution might be a suitable model for the number of failed connections every hour. [2]
\end{enumerate}
Find the probability that in a randomly chosen hour
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item all Internet users connect at their first attempt, [2]
\item more than 4 users fail to connect at their first attempt. [2]
\end{enumerate}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Write down the distribution of the number of users failing to connect at their first attempt in an 8-hour period. [1]
\item Using a suitable approximation, find the probability that 12 or more users fail to connect at their first attempt in a randomly chosen 8-hour period. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q5 [13]}}