| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Poisson hypothesis test |
| Difficulty | Standard +0.3 This is a straightforward application of standard Poisson distribution techniques: parts (a-b) are direct probability calculations from tables/formula, part (c) extends to a 3-week period (routine parameter scaling), and part (d) is a standard hypothesis test with clear structure. All techniques are textbook exercises for S2 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.05b Hypothesis test for binomial proportion2.05c Significance levels: one-tail and two-tail5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
The maintenance department of a college receives requests for replacement light bulbs at a rate of 2 per week.
Find the probability that in a randomly chosen week the number of requests for replacement light bulbs is
\begin{enumerate}[label=(\alph*)]
\item exactly 4, [2]
\item more than 5. [2]
\end{enumerate}
Three weeks before the end of term the maintenance department discovers that there are only 5 light bulbs left.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the probability that the department can meet all requests for replacement light bulbs before the end of term. [3]
\end{enumerate}
The following term the principal of the college announces a package of new measures to reduce the amount of damage to college property. In the first 4 weeks following this announcement, 3 requests for replacement light bulbs are received.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Stating your hypotheses clearly test, at the 5\% level of significance, whether or not there is evidence that the rate of requests for replacement light bulbs has decreased. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q5 [12]}}