| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Known variance confidence intervals |
| Difficulty | Standard +0.3 This is a straightforward application of known-variance confidence intervals with standard CLT justification. Part (a) requires basic formula substitution (sample mean, known SD, z-value lookup), part (b) involves simple interpretation of the CI and a proportion calculation, and part (c) tests understanding of when CLT is needed. All steps are routine S1 techniques with no novel problem-solving required, making it slightly easier than average. |
| Spec | 5.05c Hypothesis test: normal distribution for population mean5.05d Confidence intervals: using normal distribution |
7 The volume of bleach in a 5-litre bottle may be modelled by a random variable with a standard deviation of 75 millilitres.
The volume, in litres, of bleach in each of a random sample of 36 such bottles was measured. The 36 measurements resulted in a total volume of 181.80 litres and exactly 8 bottles contained less than 5 litres.
\begin{enumerate}[label=(\alph*)]
\item Construct a 98\% confidence interval for the mean volume of bleach in a 5-litre bottle.
\item It is claimed that the mean volume of bleach in a 5-litre bottle exceeds 5 litres and also that fewer than 10 per cent of such bottles contain less than 5 litres.
Comment, with numerical justification, on each of these two claims.
\item State, with justification, whether you made use of the Central Limit Theorem in constructing the confidence interval in part (a).
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2012 Q7 [9]}}