| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Explain or apply conditions in context |
| Difficulty | Moderate -0.8 This is a straightforward application of the Poisson distribution with standard calculations (parts a-c require direct use of the probability formula or tables) and a recall question about Poisson conditions (part d). While it's Further Maths content, the question requires no problem-solving insight—just routine application of formulas and knowledge of when Poisson applies (events occur independently at constant rate). |
| Spec | 5.02i Poisson distribution: random events model5.02j Poisson formula: P(X=x) = e^(-lambda)*lambda^x/x!5.02k Calculate Poisson probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | P(2 meteors) = 0.2169 |
| [1] | 1.1 | |
| 1 | (b) | P(> 3 meteors) = 1 – 0.9662 |
| = 0.0338 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Or [P(> 3 meteors) =] 1 – P(≤ 3 meteors) |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (c) | Mean = 10 × 1.2 = 12 |
| P(≤ 8 meteors) = 0.1550 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 3.3 | |
| 1.1 | BC | |
| 1 | (d) | Meteors occur randomly, independently |
| and at a uniform average rate | E1 |
| Answer | Marks |
|---|---|
| [2] | 2.2b |
| 2.4 | Allow ‘constant average rate’ and ‘same average rate’ |
Question 1:
1 | (a) | P(2 meteors) = 0.2169 | B1
[1] | 1.1
1 | (b) | P(> 3 meteors) = 1 – 0.9662
= 0.0338 | M1
A1
[2] | 1.1
1.1 | Or [P(> 3 meteors) =] 1 – P(≤ 3 meteors)
BC
1 | (c) | Mean = 10 × 1.2 = 12
P(≤ 8 meteors) = 0.1550 | B1
B1
[2] | 3.3
1.1 | BC
1 | (d) | Meteors occur randomly, independently
and at a uniform average rate | E1
E1
[2] | 2.2b
2.4 | Allow ‘constant average rate’ and ‘same average rate’
No context needed due to question giving context
Needs to have ‘constant’ oe and ‘average’ oe Not ‘overall’1 During a meteor shower, the number of meteors that can be seen at a particular location can be modelled by a Poisson distribution with mean 1.2 per minute.
\begin{enumerate}[label=(\alph*)]
\item Find the probability that exactly 2 meteors are seen in a period of 1 minute.
\item Find the probability that more than 3 meteors are seen in a period of 1 minute.
\item Find the probability that no more than 8 meteors are seen in a period of 10 minutes.
\item Explain what the fact that the number of meteors seen can be modelled by a Poisson distribution tells you about the occurrence of meteors.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2022 Q1 [7]}}