| Exam Board | AQA |
|---|---|
| Module | Further Paper 3 Statistics (Further Paper 3 Statistics) |
| Year | 2023 |
| Session | June |
| Marks | 1 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Poisson with geometric or waiting time |
| Difficulty | Moderate -0.5 This is a straightforward recall question testing knowledge of the relationship between exponential and Poisson distributions. Students need only recognize that if time between events follows Exponential(μ), then the number of events per unit time follows Poisson(1/μ), giving Poisson(0.8). It's a 1-mark multiple choice question requiring minimal calculation or reasoning. |
| Spec | 5.02i Poisson distribution: random events model |
| Distribution | Mean |
| Exponential | 0.8 |
| Exponential | 1.25 |
| Poisson | 0.8 |
| Poisson | 1.25 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Poisson, mean \(0.8\) | B1 | Ticks correct answer |
## Question 2:
| Answer | Mark | Guidance |
|--------|------|----------|
| Poisson, mean $0.8$ | B1 | Ticks correct answer |
**Question total: 1 mark**
---2 The time, $T$ days, between rain showers in a city in autumn can be modelled by an exponential distribution with mean 1.25
Find the distribution of the number of rain showers per day in the city.\\
Tick ( $\checkmark$ ) one box.\\[0pt]
[1 mark]\\
\includegraphics[max width=\textwidth, alt={}, center]{1e2fdd33-afa4-486f-a9e2-1d425ed14eee-03_108_113_1800_370}
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Distribution & Mean \\
\hline
Exponential & 0.8 \\
\hline
\end{tabular}
\end{center}
\begin{center}
\includegraphics[max width=\textwidth, alt={}]{1e2fdd33-afa4-486f-a9e2-1d425ed14eee-03_108_113_1932_370}
\end{center}
\begin{center}
\begin{tabular}{ | l | l | }
\hline
Exponential & 1.25 \\
\hline
\end{tabular}
\end{center}
□
\begin{center}
\begin{tabular}{ | c | c | }
\hline
Poisson & 0.8 \\
\hline
\end{tabular}
\end{center}
□
\begin{center}
\begin{tabular}{ | l | l | }
\hline
Poisson & 1.25 \\
\hline
\end{tabular}
\end{center}
\hfill \mbox{\textit{AQA Further Paper 3 Statistics 2023 Q2 [1]}}