| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2024 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Poisson with geometric or waiting time |
| Difficulty | Moderate -0.8 This is a straightforward Poisson distribution question requiring only standard recall and application of formulas. Parts (a) and (e) test knowledge of assumptions, (b) and (c) are direct calculator computations with given parameters, and (d) involves recognizing the exponential distribution connection—all routine A-level statistics content with no problem-solving insight required. |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
A baker sells 3-5 birthday cakes per hour on average.
\begin{enumerate}[label=(\alph*)]
\item State, in context, \textbf{two} assumptions you would have to make in order to model the number of birthday cakes sold using a Poisson distribution. [1]
\item Using a Poisson distribution and showing your calculation, find the probability that exactly 2 birthday cakes are sold in a randomly selected 1-hour period. [2]
\item Calculate the probability that, during a randomly selected 3-hour period, the baker sells more than 10 birthday cakes. [3]
\item The baker sells a birthday cake at 9:30 a.m. Calculate the probability that the baker will sell the next birthday cake before 10:00 a.m. [3]
\item Select one of the assumptions in part (a) and comment on its reasonableness. [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 2024 Q2 [10]}}