| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Explain or apply conditions in context |
| Difficulty | Standard +0.3 Part (a) involves straightforward application of Poisson distribution tables/calculator with given parameters (λ=12 and λ=60), requiring only routine probability calculations. Part (b) tests understanding of Poisson conditions (independence, constant rate) but is a standard bookwork question. This is slightly easier than average as it's mostly recall and direct application with no problem-solving or novel 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 probabilities5.02l Poisson conditions: for modelling5.02m Poisson: mean = variance = lambda |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | (i) |
| = 0.1556 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Allow M1 for use of 1 – P(≤14) with λ = 12 giving |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | (ii) |
| P(<50) = 0.0844 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1b |
| 1.1 | Allow P(X≤50) = 0.10767... for M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | Electrons pass randomly and independently |
| and at a uniform average rate | E1 |
| Answer | Marks |
|---|---|
| [2] | 2.2a |
Question 4:
4 | (a) | (i) | P(>15) = 1 – 0.8444
= 0.1556 | M1
A1
[2] | 1.1
1.1 | Allow M1 for use of 1 – P(≤14) with λ = 12 giving
0.22797… or
1 – P(≤16) which gives 0.1013
BC
4 | (a) | (ii) | Poisson(60)
P(<50) = 0.0844 | M1
A1
[2] | 3.1b
1.1 | Allow P(X≤50) = 0.10767... for M1
BC
4 | (b) | Electrons pass randomly and independently
and at a uniform average rate | E1
E1
[2] | 2.2a
2.2a4 It is known that in an electronic circuit, the number of electrons passing per nanosecond can be modelled by a Poisson distribution. In a particular electronic circuit, the mean number of electrons passing per nanosecond is 12 .
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Determine the probability that there are more than 15 electrons passing in a randomly selected nanosecond.
\item Determine the probability that there are fewer than 50 electrons passing in a randomly selected period of 5 nanoseconds.
\end{enumerate}\item Explain what you can deduce about the electrons passing in the circuit from the fact that a Poisson distribution is a suitable model.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2021 Q4 [6]}}