| Exam Board | OCR MEI |
|---|---|
| Module | Further Statistics A AS (Further Statistics A AS) |
| Year | 2024 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Identify distribution and parameters |
| Difficulty | Moderate -0.8 This is a straightforward binomial distribution question requiring identification of the distribution (part a), basic probability calculations using the binomial formula or tables (part b), and a slightly more involved calculation combining binomial probability with ordering (part c). All parts are standard textbook exercises with no novel problem-solving required, making it easier than average for A-level. |
| Spec | 5.02d Binomial: mean np and variance np(1-p) |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | (i) |
| Answer | Marks |
|---|---|
| probability). | M1 |
| Answer | Marks |
|---|---|
| [3] | 1.1a |
| Answer | Marks |
|---|---|
| 2.1 | B(10, 0.43) is M1A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (a) | (ii) |
| Answer | Marks | Guidance |
|---|---|---|
| sample is) selected randomly. | B1 | |
| [1] | 2.4 | Must refer to withdrawals. |
| 6 | (b) | (i) |
| [1] | 1.1 | 0.2462307291... |
| 6 | (b) | (ii) |
| [1] | 1.1 | 0.1401294608... |
| 6 | (b) | (iii) |
| 1 – 0.7792942284 = awrt 0.221 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1b |
| 1.1 | Or P(Y 4) where Y is the no. |
| Answer | Marks | Guidance |
|---|---|---|
| 6 | (c) | Use of B(9, 0.43) or B(9, 0.57) |
| 0.570.22905... = awrt 0.131 | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1b |
| 1.1 | Can be implied by correct answer. |
Question 6:
6 | (a) | (i) | B or bin or binomial
with n = 10 and p = 0.43
A trial comprises looking at a withdrawal and
determining whether it is small or large. There is
a fixed number of these and each must result in
exactly one of these two outcomes (with constant
probability). | M1
A1
B1
[3] | 1.1a
3.3
2.1 | B(10, 0.43) is M1A1
Fixed number of trials, each trial
has only two possible outcomes.
6 | (a) | (ii) | We must assume that each withdrawal is
independent of other withdrawals.
or
We must assume that the 10 withdrawals are (or
sample is) selected randomly. | B1
[1] | 2.4 | Must refer to withdrawals.
6 | (b) | (i) | awrt 0.246 | B1
[1] | 1.1 | 0.2462307291...
6 | (b) | (ii) | awrt 0.140 | B1
[1] | 1.1 | 0.1401294608...
6 | (b) | (iii) | If X is the no. small withdrawals, P(X ≥ 6)
1 – 0.7792942284 = awrt 0.221 | M1
A1
[2] | 3.1b
1.1 | Or P(Y 4) where Y is the no.
large.
Can be implied by correct answer.
0.2207057716...
(could be direct from B(10, 0.57))
6 | (c) | Use of B(9, 0.43) or B(9, 0.57)
0.570.22905... = awrt 0.131 | M1
A1
[2] | 3.1b
1.1 | Can be implied by correct answer.
PMT
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Please get in touch if you want to discuss the accessibility of resources we offer to support you in delivering our qualifications.6 A bank monitors the amounts of cash withdrawn from a cash machine. It categorises any withdrawal of an amount of $\pounds 50$ or less as 'small' and any withdrawal of an amount greater than $\pounds 50$ as 'large'.
Over a long period of time the bank finds that the proportion of withdrawals that are small is 0.43 .\\
The bank wishes to model a sample of 10 withdrawals to examine the number of small withdrawals.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item State a suitable probability distribution for such a model, justifying your answer.
\item State one assumption needed for the model to be valid.
\end{enumerate}\item \begin{enumerate}[label=(\roman*)]
\item Find the probability that exactly 4 of the 10 withdrawals are small.
\item Find the probability that exactly 4 of the 10 withdrawals are large.
\item Find the probability that no more than 4 of the 10 withdrawals are large.
\end{enumerate}\item Find the probability that, in the 10 withdrawals, the 7th withdrawal is large and there are exactly 3 that are small.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Statistics A AS 2024 Q6 [10]}}