| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Single scaled time period |
| Difficulty | Moderate -0.8 This is a straightforward application of standard Poisson distribution properties and calculations. Parts (i) and (iii) test basic recall (variance equals mean, scaling property), while parts (ii) and (iv) require routine use of the Poisson probability formula with no conceptual challenges or problem-solving insight needed. |
| 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 |
|---|---|---|
| 1 | (i) | Variance = 0.45 |
| [1] | 1.2 | |
| (ii) | P(2 failures) = 0.0646 | B1 |
| [1] | 1.1 | BC |
| (iii) | Poisson | |
| Parameter = 1.8 | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.1a | N |
| (iv) | Using λ = 1.8 |
| Answer | Marks |
|---|---|
| = 0.5372 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1a |
| 1.1 | E |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | 1 | 2 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(i) | 1 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(ii) | 1 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(iii) | 1 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(iv) | 2 | 0 |
Question 1:
1 | (i) | Variance = 0.45 | B1
[1] | 1.2
(ii) | P(2 failures) = 0.0646 | B1
[1] | 1.1 | BC
(iii) | Poisson
Parameter = 1.8 | B1
B1
[2] | 3.3
1.1a | N
(iv) | Using λ = 1.8
P(at least 2 in 4 weeks) = 1 – 0.4628
= 0.5372 | M1
A1
[2] | 1.1a
1.1 | E
For 0.4628 OR 1 - P(Y ≤ 1)
BC cao
1 | 1 | 2 | 3 | 4 | 5 | 6
--- 1(i) ---
1(i) | 1 | 0 | 0 | 0 | 1
--- 1(ii) ---
1(ii) | 1 | 0 | 0 | 0 | 1
--- 1(iii) ---
1(iii) | 1 | 0 | 0 | 1 | 2
--- 1(iv) ---
1(iv) | 2 | 0 | 0 | 0 | 21 The number of failures of a machine each week at a factory is modelled by a Poisson distribution with mean 0.45.\\
(i) Write down the variance of the distribution.\\
(ii) Find the probability that there are exactly 2 failures in a week.\\
(iii) State a distribution which can be used to model the number of failures in a period of 4 weeks.\\
(iv) Find the probability that there are at least 2 failures in a period of 4 weeks.
\hfill \mbox{\textit{OCR MEI Further Statistics A AS Q1 [6]}}