| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Probability within standard deviations |
| Difficulty | Moderate -0.8 This is a straightforward application of uniform distribution formulas. Part (a) requires only stating the distribution name, while part (b) involves calculating mean and standard deviation using standard formulas, then finding the probability within one SD—all routine procedures with no problem-solving insight required. |
| Spec | 5.02e Discrete uniform distribution |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (a) | (Discrete) Uniform (distribution). |
| (On the values) {1, 2, …, 50} | B1* |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.2 | For uniform |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | (b) | E(X) = 25.5 |
| Answer | Marks |
|---|---|
| 50 | B1 |
| Answer | Marks |
|---|---|
| [4] | 1.1a |
| Answer | Marks |
|---|---|
| 1.1 | For correct variance or standard deviation |
Question 4:
4 | (a) | (Discrete) Uniform (distribution).
(On the values) {1, 2, …, 50} | B1*
B1dep*
[2] | 3.3
1.2 | For uniform
For values
SC B1 if ‘uniform’ is not stated but correct probability
distribution is seen
4 | (b) | E(X) = 25.5
Var(X) = 208.25 (s.d. = 14.4 oe)
Need (11.1 < X < 39.9) 12 ≤ X ≤ 39
= 28 =0.56
50 | B1
B1
M1
A1
[4] | 1.1a
1.1
3.1a
1.1 | For correct variance or standard deviation
For finding their E(X) ± their s.d., giving appropriate
integer bounds.
cao www4 A random number generator generates integers between 1 and 50 inclusive, with each number having an equal probability of being generated.
\begin{enumerate}[label=(\alph*)]
\item State the probability distribution of the numbers generated.
\item Determine the probability that a number generated is within one standard deviation of the mean.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2022 Q4 [6]}}