| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2022 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single period normal approximation - scaled period (normal approximation only) |
| Difficulty | Easy -1.2 Part (a) requires recall of standard Poisson conditions (no problem-solving), while parts (b) and (c) involve routine Poisson probability calculations using tables or calculators. The normal approximation in (c) is a standard technique. This is easier than average as it tests basic recall and straightforward application of formulas. |
| 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 |
|---|---|---|
| 2 | (a) | Breakdowns occur randomly, independently |
| and at a uniform average rate | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 3.3 | |
| 3.3 | Allow ‘constant average rate’ | |
| 2 | (b) | (i) |
| [1] | 1.1 | BC awrt 0.0636. Allow 0.064 |
| 2 | (b) | (ii) |
| = 0.5068 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1a |
| 1.1 | BC M1 for attempt to find 1 – P(X < 2) |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (c) | Mean = 52 × 1.7 (= 88.4) |
| P(less than 100) = 0.8799 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | BC Allow 0.880, 0.88 |
Question 2:
2 | (a) | Breakdowns occur randomly, independently
and at a uniform average rate | E1
E1
[2] | 3.3
3.3 | Allow ‘constant average rate’
2 | (b) | (i) | P(exactly 4) = 0.0636 | B1
[1] | 1.1 | BC awrt 0.0636. Allow 0.064
2 | (b) | (ii) | P(at least 2) = 1 – 0.4932
= 0.5068 | M1
A1
[2] | 1.1a
1.1 | BC M1 for attempt to find 1 – P(X < 2)
Allow awrt 0.507, 0.51
2 | (c) | Mean = 52 × 1.7 (= 88.4)
P(less than 100) = 0.8799 | M1
A1
[2] | 1.1
1.1 | BC Allow 0.880, 0.882 On a car assembly line, a robot is used for a particular task.
\begin{enumerate}[label=(\alph*)]
\item State the conditions under which a Poisson distribution is an appropriate model for the number of breakdowns of the robot in a week.
It is given that the average number of breakdowns of the robot in a week is 1.7 . For the remainder of this question, you should assume that a Poisson distribution is an appropriate model for the number of breakdowns of the robot in a week.
\item \begin{enumerate}[label=(\roman*)]
\item Find the probability that the number of breakdowns of the robot in a week is exactly 4.
\item Determine the probability that the number of breakdowns of the robot in a week is at least 2 .
\end{enumerate}\item Determine the probability that the number of breakdowns of the robot in 52 weeks is less than 100.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2022 Q2 [7]}}