| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2024 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Poisson distribution |
| Type | Poisson parameter from given probability |
| Difficulty | Standard +0.3 This is a straightforward Poisson distribution question requiring standard techniques: using the variance property (σ² = λ) to find the parameter, then applying the probability mass function and cumulative distribution function. The scaling to a 20-minute period is routine. While it requires multiple steps, each is a direct application of textbook methods with no novel 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 modelling |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (a) | Variance = 0.36 |
| Mean = 0.36 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 3.3 | |
| 1.1 | soi | |
| 2 | (b) | (i) |
| [1] | 3.4 | BC FT their mean |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (b) | (ii) |
| = 0.0512 | M1 |
| Answer | Marks |
|---|---|
| [2] | 1.1 |
| 1.1 | Or [P(X > 1) =] 1 – P(X ≤ 1) |
| Answer | Marks | Guidance |
|---|---|---|
| 2 | (c) | Mean = 20×𝑡ℎ𝑒𝑖𝑟 0.36 [= 7.2] |
| P(Y < 5) = 0.1555 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.1 | BC FT their mean |
Question 2:
2 | (a) | Variance = 0.36
Mean = 0.36 | M1
A1
[2] | 3.3
1.1 | soi
2 | (b) | (i) | P(X = 1) = 0.2512 | B1
[1] | 3.4 | BC FT their mean
Mean = 0.6 P(X = 1) = 0.3293
2 | (b) | (ii) | P(X > 1) = 1−0.9488
= 0.0512 | M1
A1
[2] | 1.1
1.1 | Or [P(X > 1) =] 1 – P(X ≤ 1)
FT their mean
Mean = 0.6 P(X > 1) = 1−0.8781 = 0.1219
2 | (c) | Mean = 20×𝑡ℎ𝑒𝑖𝑟 0.36 [= 7.2]
P(Y < 5) = 0.1555 | M1
A1
[2] | 3.3
1.1 | BC FT their mean
Mean = 0.6 P(Y < 5) = 0.00762 The number of cars arriving per minute to queue at a drive-through fast-food restaurant is modelled by the random variable $X$. The standard deviation of $X$ is 0.6 . You should assume that arrivals are random and independent and occur at a constant average rate.
\begin{enumerate}[label=(\alph*)]
\item Find the mean of $X$.
\item \begin{enumerate}[label=(\roman*)]
\item Calculate $\mathrm { P } ( X = 1 )$.
\item Calculate $\mathrm { P } ( X > 1 )$.
\end{enumerate}\item Find the probability that fewer than 5 cars arrive in a randomly chosen 20 -minute period.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2024 Q2 [9]}}