| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2004 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Unknown variance confidence intervals |
| Difficulty | Moderate -0.3 This is a straightforward application of standard S3 formulas: calculating unbiased estimates (sample mean and variance with n-1 denominator), then constructing a confidence interval using the normal approximation with known sample variance. The large sample size (n=100) makes the CLT application routine, and all three parts require direct formula application with no problem-solving or conceptual challenges beyond standard textbook exercises. |
| Spec | 5.05b Unbiased estimates: of population mean and variance5.05d Confidence intervals: using normal distribution |
4. Kylie regularly travels from home to visit a friend. On 10 randomly selected occasions the journey time $x$ minutes was recorded. The results are summarised as follows.
$$\Sigma x = 753 , \quad \Sigma x ^ { 2 } = 57455 .$$
\begin{enumerate}[label=(\alph*)]
\item Calculate unbiased estimates of the mean and the variance of the population of journey times.
After many journeys, a random sample of 100 journeys gave a mean of 74.8 minutes and a variance of 84.6 minutes ${ } ^ { 2 }$.
\item Calculate a 95\% confidence interval for the mean of the population of journey times.
\item Write down two assumptions you made in part (b).
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2004 Q4 [10]}}