| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2006 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Normal Distribution |
| Type | Single tail probability P(X < a) or P(X > a) |
| Difficulty | Moderate -0.3 This is a standard confidence interval question with straightforward calculations using given σ=6 and n=10. Part (a) requires computing sample mean and applying z-critical values, part (b) tests understanding of confidence interval interpretation. While multi-part, each component is routine S1 material requiring no novel insight—slightly easier than average due to clear structure and standard techniques. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.05c Hypothesis test: normal distribution for population mean |
4 The weights of packets of sultanas may be assumed to be normally distributed with a standard deviation of 6 grams.
The weights of a random sample of 10 packets were as follows:\\
$\begin{array} { l l l l l l l l l l } 498 & 496 & 499 & 511 & 503 & 505 & 510 & 509 & 513 & 508 \end{array}$
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Construct a $99 \%$ confidence interval for the mean weight of packets of sultanas, giving the limits to one decimal place.
\item State why, in calculating your confidence interval, use of the Central Limit Theorem was not necessary.
\item On each packet it states 'Contents 500 grams'.
Comment on this statement using both the given sample and your confidence interval.
\end{enumerate}\item Given that the mean weight of all packets of sultanas is 500 grams, state the probability that a 99\% confidence interval for the mean, calculated from a random sample of packets, will not contain 500 grams.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2006 Q4 [7]}}