| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics Major (Further Statistics Major) |
| Year | 2024 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Probability Distributions and Random Variables |
| Type | Find median or percentiles |
| Difficulty | Standard +0.3 This is a straightforward continuous probability distribution question requiring standard techniques: finding a constant by integrating to 1, calculating a probability by integration, and finding the median by solving F(x) = 0.5. All steps are routine A-level Further Maths procedures with no conceptual challenges, making it slightly easier than average. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03f Relate pdf-cdf: medians and percentiles |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | 1 |
| Answer | Marks |
|---|---|
| 1250 | M1 |
| Answer | Marks |
|---|---|
| [2] | 2.1 |
| 1.1 | 5 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | 1 1 |
| Answer | Marks |
|---|---|
| 100 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.4 |
| 1.1 | 5 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (c) | 1 1 1 |
| Answer | Marks |
|---|---|
| 𝑚 = 35.4 or 25√2 (35.35533…) aef | M1 |
| Answer | Marks |
|---|---|
| [3] | 2.1 |
| Answer | Marks |
|---|---|
| 1.1 | 𝑚 1 |
Question 4:
4 | (a) | 1
×50×50𝑎=1
2
1
𝑎 =
1250 | M1
A1
[2] | 2.1
1.1 | 5
Or by integration ∫ 𝑎𝑥d𝑥 = 1
0
4 | (b) | 1 1
P(X ≤ 5) = × ×5×5
2 1250
1
=
100 | M1
A1
[2] | 3.4
1.1 | 5 1
Or by integration ∫ 𝑥d𝑥 Using their a
0 1250
4 | (c) | 1 1 1
× ×𝑚×𝑚 =
2 1250 2
𝑚2 = 1250
𝑚 = 35.4 or 25√2 (35.35533…) aef | M1
M1
A1
[3] | 2.1
1.1
1.1 | 𝑚 1
Or by integration ∫ 𝑥d𝑥 Using their a
0 1250
Using their a 𝑚2 = 1
their 𝑎4 An archer fires arrows at a circular target of radius 50 cm . The distance in cm that an arrow lands from the centre of the target is modelled by the random variable $X$, with probability density function given by\\
$f ( x ) = \begin{cases} a x & 0 \leqslant x \leqslant 50 , \\ 0 & \text { otherwise, } \end{cases}$\\
where $a$ is a constant.
\begin{enumerate}[label=(\alph*)]
\item Determine the value of $a$.
\item Determine the probability that an arrow will land within 5 cm of the centre of the target.
\item Determine the median distance from the centre of the target that an arrow will land.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics Major 2024 Q4 [7]}}