| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Minor (Further Statistics Minor) |
| Year | 2021 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Calculate basic probabilities |
| Difficulty | Standard +0.3 This is a straightforward application of discrete uniform distribution properties. Part (a) requires basic counting and probability calculation with simple floor function considerations, while part (b) involves standard formulas for mean and standard deviation of uniform distributions. The question is slightly above average due to the algebraic manipulation in (a)(ii) and the need to recall/derive uniform distribution formulas, but remains a standard textbook exercise with no novel problem-solving required. |
| Spec | 5.02e Discrete uniform distribution5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | (i) |
| Answer | Marks | Guidance |
|---|---|---|
| 4 4 | B1 | |
| [1] | 3.3 | |
| 6 | (a) | (ii) |
| Answer | Marks |
|---|---|
| 4n | M1 |
| Answer | Marks |
|---|---|
| [3] | 2.2a |
| Answer | Marks |
|---|---|
| 1.1 | Single fraction |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (b) | E(X) = 51 Var(X) = 850 |
| Answer | Marks |
|---|---|
| 101 | M1 |
| Answer | Marks |
|---|---|
| [3] | 3.1b |
| Answer | Marks |
|---|---|
| 1.1 | For either |
Question 6:
6 | (a) | (i) | Uniform distribution on {1, 2, … , n}
P ( X ≤ 1n )= 1
4 4 | B1
[1] | 3.3
6 | (a) | (ii) | k
P ( X ≤ 1n )=
4 4k+1
1(n−1)
= 4
n
n−1
=
4n | M1
M1
A1
[3] | 2.2a
1.1
1.1 | Single fraction
required for A1
6 | (b) | E(X) = 51 Var(X) = 850
SD(X) = 29.1 So require P(21.9 < X < 80.1)
P(22≤ X ≤80)= 59
101 | M1
M1
A1
[3] | 3.1b
1.1a
1.1 | For either
For required interval
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recorded or monitored6 A lottery has tickets numbered 1 to $n$ inclusive, where $n$ is a positive integer. The random variable $X$ denotes the number on a ticket drawn at random.
\begin{enumerate}[label=(\alph*)]
\item Determine $\mathrm { P } \left( \mathrm { X } \leqslant \frac { 1 } { 4 } \mathrm { n } \right)$ in each of the following cases.
\begin{enumerate}[label=(\roman*)]
\item $n$ is a multiple of 4 .
\item $n$ is of the form $4 k + 1$, where $k$ is a positive integer. Give your answer as a single fraction in terms of $n$.
\end{enumerate}\item Given that $n = 101$, find the probability that $X$ is within one standard deviation of the mean.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2021 Q6 [7]}}