| Exam Board | WJEC |
|---|---|
| Module | Unit 4 (Unit 4) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Verify conditions in context |
| Difficulty | Easy -1.2 This question tests basic understanding of binomial distribution assumptions and qualitative properties of probability distributions. Part (a) requires recall of standard binomial assumptions with minimal application to context. Part (b) asks for simple observations about distribution shape/spread from given diagrams—no calculations or deep reasoning required. This is substantially easier than average A-level questions which typically require multi-step calculations or problem-solving. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
At a fairground, Kirsty throws $n$ balls in order to try to knock coconuts off their stands. Any coconuts she knocks off are replaced before she throws again. Kirsty counts the number of coconuts she successfully knocks off their stands. On average, she knocks off a coconut with 20\% of her throws.
\begin{enumerate}[label=(\alph*)]
\item What assumptions are needed in order to model this situation with a binomial distribution? Explain whether these assumptions are reasonable. [2]
\end{enumerate}
Kirsty uses a spreadsheet to produce the following diagrams, showing the probability distributions of the number of coconuts knocked off their stands for different values of $n$.
\includegraphics{figure_3}
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Describe two ways in which the distribution changes as $n$ increases. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 2019 Q3 [4]}}