| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2003 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Confidence intervals |
| Type | Calculate CI from summary stats |
| Difficulty | Moderate -0.5 This is a straightforward confidence interval calculation using the normal distribution with a given sample mean and standard deviation. Part (a) requires direct application of the standard formula with z=2.576, while part (b) asks for a simple interpretation when the true mean falls outside the interval. The question is slightly easier than average because it's a routine textbook exercise with no conceptual complications, though it does require knowledge of the appropriate z-value and the assumption that either the population is normal or the CLT applies. |
| Spec | 5.05d Confidence intervals: using normal distribution |
2. A random sample of 30 apples was taken from a batch. The mean weight of the sample was 124 g with standard deviation 20 g .
\begin{enumerate}[label=(\alph*)]
\item Find a $99 \%$ confidence interval for the mean weight $\mu$ grams of the population of apples. Write down any assumptions you made in your calculations.
Given that the actual value of $\mu$ is 140 ,
\item state, with a reason, what you can conclude about the sample of 30 apples.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2003 Q2 [8]}}