| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics B AS (Further Statistics B AS) |
| Session | Specimen |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Comparing two journey times |
| Difficulty | Standard +0.3 This is a straightforward application of standard results for linear combinations of normal random variables. Part (i) requires finding P(Bus < Cycle) by considering the difference of two normals; part (ii) uses the sum of normals; part (iii) is a standard commentary question. All techniques are direct applications of taught methods with no novel insight required, making it slightly easier than average. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.04b Linear combinations: of normal distributions |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (i) | E |
| Answer | Marks |
|---|---|
| Probability(time difference < 0) = 0.376 | B1 |
| Answer | Marks |
|---|---|
| [3] | 3.3 |
| Answer | Marks |
|---|---|
| 1.1 | For Normal and mean |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (ii) | P |
Total for 5 bus journeys N(115, 180)
| Answer | Marks |
|---|---|
| Probability(total time < 2 hours) = 0.645 | B1 |
| Answer | Marks |
|---|---|
| [2] | 3.4 |
| 1.1 | For both |
| Answer | Marks | Guidance |
|---|---|---|
| 7 | (iii) | S |
| Answer | Marks | Guidance |
|---|---|---|
| days in a row | E1 | |
| [1] | 3.5b | |
| Question | AO1 | AO2 |
| 1iA | 1 | 0 |
| iB | 1 | 0 |
| 1ii | 0 | 0 |
| 1iii | 1 | 0 |
| 1iv | 2 | 0 |
| 2i | 2 | 0 |
| 2ii | 2 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2iii | 2 | 0 |
| 3i | 1 | 1 |
| 0 | 2 | |
| 3ii | 2 | 0 |
| 3iii | 6 | 0 |
| 4i | 1 | 0 |
| 0 | 0 | 1 |
| 4ii | 3 | 1 |
| 5i | 2 | 1 |
| 0 | 0 | 3 |
| 5ii | 1 | 0 |
| 5iiiA | 1 | C |
| 0 | 0 | 0 |
| 5iiiB | 0 | 1 |
| 5iv | E | |
| 0 | 1 | 0 |
| 5vA | 1 | 0 |
| 5vB | 1 | 0 |
| 5vi | P | |
| 0 | 0 | 0 |
| 6i | 3 | 0 |
| Answer | Marks | Guidance |
|---|---|---|
| 6ii | 0 | 2 |
| 6iii | 1 | 0 |
| 7i | 2 | 0 |
| 7ii | 1 | 0 |
| 7iii | 0 | 0 |
| Total | 37 | 8 |
Question 7:
7 | (i) | E
s time – c cle time ( 40)
Probability(time difference < 0) = 0.376 | B1
B1
B1
[3] | 3.3
1.1
1.1 | For Normal and mean
For variance
BC
7 | (ii) | P
Total for 5 bus journeys N(115, 180)
Probability(total time < 2 hours) = 0.645 | B1
B1
[2] | 3.4
1.1 | For both
BC
7 | (iii) | S
Sensible comment
e.g.
(cid:120) Factors which delay a bus journey might
delay a bicycle journey
(cid:120) Roadworks might cause delays on several
days in a row | E1
[1] | 3.5b
Question | AO1 | AO2 | AO3(PS) | AO3(M) | Total
1iA | 1 | 0 | 0 | 0 | 1
iB | 1 | 0 | 0 | 1 | 2
1ii | 0 | 0 | 0 | 1 | 1
1iii | 1 | 0 | 0 | 1 | 2
1iv | 2 | 0 | 0 | 1 | 3
2i | 2 | 0 | 0 | 0 | 2
2ii | 2 | 1 | 0 | 0 | N
3
2iii | 2 | 0 | 0 | 0 | 2
3i | 1 | 1 | 0 | E
0 | 2
3ii | 2 | 0 | 0 | 1 | 3
3iii | 6 | 0 | 0 | 0 | 6
4i | 1 | 0 | M
0 | 0 | 1
4ii | 3 | 1 | 0 | 3 | 7
5i | 2 | 1 | I
0 | 0 | 3
5ii | 1 | 0 | 0 | 0 | 1
5iiiA | 1 | C
0 | 0 | 0 | 1
5iiiB | 0 | 1 | 0 | 0 | 1
5iv | E
0 | 1 | 0 | 1 | 2
5vA | 1 | 0 | 0 | 0 | 1
5vB | 1 | 0 | 0 | 0 | 1
5vi | P
0 | 0 | 0 | 1 | 1
6i | 3 | 0 | 0 | 1 | 4
S
6ii | 0 | 2 | 0 | 0 | 2
6iii | 1 | 0 | 1 | 0 | 2
7i | 2 | 0 | 0 | 1 | 3
7ii | 1 | 0 | 0 | 1 | 2
7iii | 0 | 0 | 0 | 1 | 1
Total | 37 | 8 | 1 | 14 | 607 Two flatmates work at the same location. One of them takes the bus to work and the other one cycles. Journey times, measured in minutes, are distributed as follows.
\begin{itemize}
\item By bus: Normally distributed with mean 23 and standard deviation 6
\item By bicycle: Normally distributed with mean 21 and standard deviation 2
\end{itemize}
You should assume that all journey times are independent.\\
(i) One morning the two flatmates set out at the same time. Find the probability that the person who takes the bus arrives before the cyclist.\\
(ii) Find the probability that the total time taken for 5 bus journeys is less than 2 hours.\\
(iii) Comment on the assumption that all journey times are independent.
\section*{END OF QUESTION PAPER}
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\hfill \mbox{\textit{OCR MEI Further Statistics B AS Q7 [6]}}