| Exam Board | AQA |
|---|---|
| Module | Paper 3 (Paper 3) |
| Session | Specimen |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Direct binomial probability calculation |
| Difficulty | Moderate -0.8 Part (a) is a direct application of the binomial probability formula with given n=25, p=1680/2400=0.7, and x=22—purely computational with no conceptual challenge. Part (b) requires recognizing that households on the same street likely aren't independent (a basic understanding of binomial assumptions), but this is a standard textbook consideration. Overall, this is easier than average: straightforward calculation plus routine recall of distribution assumptions. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| 9(a) | Finds value for p | AO1.1a |
| Answer | Marks | Guidance |
|---|---|---|
| from calculator | AO1.1b | A1 |
| Answer | Marks |
|---|---|
| (b) | Explains the reason why |
| Answer | Marks | Guidance |
|---|---|---|
| apply in context | AO3.5b | E1 |
| Answer | Marks | Guidance |
|---|---|---|
| Total | 3 | |
| Q | Marking Instructions | AO |
Question 9:
--- 9(a) ---
9(a) | Finds value for p | AO1.1a | M1 | 1680
p= =0.7
2400
Finds correct probability
from calculator | AO1.1b | A1 | Using X ~ B(25,0.7),
P(X = 22) = 0.0243
(b) | Explains the reason why
the model may no longer
apply in context | AO3.5b | E1 | It is likely that all the houses (and
gardens) will be of similar types, and
hence similar owners, so not likely to
be independent as binomial model
requires.
Total | 3
Q | Marking Instructions | AO | Marks | Typical SolutionA survey has found that, of the 2400 households in Growmore, 1680 eat home-grown fruit and vegetables.
\begin{enumerate}[label=(\alph*)]
\item Using the binomial distribution, find the probability that, out of a random sample of 25 households in Growmore, exactly 22 eat home-grown fruit and vegetables. [2 marks]
\item Give a reason why you would not expect your calculation in part (a) to be valid for the 25 households in Gifford Terrace, a residential road in Growmore. [1 mark]
\end{enumerate}
\hfill \mbox{\textit{AQA Paper 3 Q9 [3]}}