| Exam Board | AQA |
|---|---|
| Module | AS Paper 2 (AS Paper 2) |
| Year | 2023 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | E(X) and Var(X) with probability calculations |
| Difficulty | Easy -1.3 This is a straightforward binomial distribution question requiring only direct application of standard formulas and calculator functions. Part (a) uses μ=np, parts (b)-(d) require calculator computation of binomial probabilities with clearly stated parameters (n=30, p=0.79). No problem-solving, interpretation, or conceptual understanding beyond basic binomial distribution recall is needed. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| 17(a) | Obtains correct mean | |
| CAO | 3.4 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 17(b) | States correct answer | |
| AWRT 0.12 | 3.4 | B1 |
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks | Guidance |
|---|---|---|
| 17(c) | States correct answer | |
| AWRT 0.014 | 3.4 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Subtotal | 1 | |
| Q | Marking instructions | AO |
| Answer | Marks |
|---|---|
| 17(d) | States or finds 1 – P(X ≤ 25 or |
| Answer | Marks | Guidance |
|---|---|---|
| AWRT 0.21(5) | 3.4 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| AWRT 0.098 | 1.1b | A1 |
| Subtotal | 2 | |
| Question 17 Total | 5 | |
| Q | Marking instructions | AO |
Question 17:
--- 17(a) ---
17(a) | Obtains correct mean
CAO | 3.4 | B1 | Mean = 30 × 0.79
= 23.7
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 17(b) ---
17(b) | States correct answer
AWRT 0.12 | 3.4 | B1 | 0.124
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 17(c) ---
17(c) | States correct answer
AWRT 0.014 | 3.4 | B1 | P(X ≤ 18) = 0.01399
= 0.014
Subtotal | 1
Q | Marking instructions | AO | Marks | Typical solution
--- 17(d) ---
17(d) | States or finds 1 – P(X ≤ 25 or
26)
PI by correct answer or
AWRT 0.21(5) | 3.4 | M1 | P(X > 26) = P(X ≥ 27)
= 1 – P(X ≤ 26)
= 1 – 0.9015596
= 0.0984404
= 0.0984
Obtains correct answer
AWRT 0.098 | 1.1b | A1
Subtotal | 2
Question 17 Total | 5
Q | Marking instructions | AO | Marks | Typical solutionAn archer is training for the Olympics.
Each of the archer's training sessions consists of 30 attempts to hit the centre of a target.
The archer consistently hits the centre of the target with 79% of their attempts.
It can be assumed that the number of times the centre of the target is hit in any training session can be modelled by a binomial distribution.
\begin{enumerate}[label=(\alph*)]
\item Find the mean of the number of times that the archer hits the centre of the target during a training session. [1 mark]
\item Find the probability that the archer hits the centre of the target exactly 22 times during a particular training session. [1 mark]
\item Find the probability that the archer hits the centre of the target 18 times or less during a particular training session. [1 mark]
\item Find the probability that the archer hits the centre of the target more than 26 times in a training session. [2 marks]
\end{enumerate}
\hfill \mbox{\textit{AQA AS Paper 2 2023 Q17 [5]}}