| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2021 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Uniform Distribution |
| Type | Variance of sum of independent values |
| Difficulty | Moderate -0.3 This is a straightforward application of discrete uniform distribution properties. Part (a) is immediate recognition, part (b) requires basic probability calculation with complementary events, and part (c) applies the standard result that Var(sum) = sum of variances for independent variables. All techniques are routine for Further Statistics students with no novel problem-solving required. |
| Spec | 2.04a Discrete probability distributions2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities5.02e Discrete uniform distribution |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (a) | Uniform |
| On the values {0, 1, 2, 3, 4} | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.3 |
| 1.2 | For uniform stated |
| Answer | Marks | Guidance |
|---|---|---|
| 5 | (b) | 2 3 3 2 |
| Answer | Marks |
|---|---|
| 25 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| [2] | 3.1a | |
| 1.1 | For at least one correct pair | |
| 5 | (c) | 52−1 |
| Answer | Marks |
|---|---|
| So variance for 5 spins = 10 | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.1 |
Question 5:
5 | (a) | Uniform
On the values {0, 1, 2, 3, 4} | B1
B1
[2] | 3.3
1.2 | For uniform stated
For values – these can be listed in a table
5 | (b) | 2 3 3 2
× + ×
5 5 5 5
12
=
25 | M1
A1
[2] | 3.1a
1.1 | For at least one correct pair
5 | (c) | 52−1
Variance for 1 spin =
12
= 2
So variance for 5 spins = 10 | M1
A1
A1
[3] | 1.1
1.1
1.15 A fair spinner has five faces, labelled 0, 1, 2, 3, 4.
\begin{enumerate}[label=(\alph*)]
\item State the distribution of the score when the spinner is spun once.
\item Determine the probability that, when the spinner is spun twice, one of the scores is less than 2 and the other is at least 2.
\item Find the variance of the total score when the spinner is spun 5 times.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2021 Q5 [7]}}