| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2018 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Unknown variance confidence intervals |
| Difficulty | Challenging +1.2 This question requires applying the Central Limit Theorem to a uniform distribution and constructing a confidence interval, but the steps are fairly standard for S3. Part (a) involves routine calculation of mean and variance of a uniform distribution, then applying CLT. Part (b) requires recognizing that the maximum value is a+6 and working backwards through the confidence interval, which adds modest problem-solving beyond pure recall but remains within typical S3 scope. |
| Spec | 5.01a Permutations and combinations: evaluate probabilities5.05d Confidence intervals: using normal distribution |
6. The continuous random variable $Y$ is uniformly distributed over the interval
$$[ a - 3 , a + 6 ]$$
where $a$ is a constant.
A random sample of 60 observations of $Y$ is taken.\\
Given that $\bar { Y } = \frac { \sum _ { i = 1 } ^ { 60 } Y _ { i } } { 60 }$
\begin{enumerate}[label=(\alph*)]
\item use the Central Limit Theorem to find an approximate distribution for $\bar { Y }$
Given that the 60 observations of $Y$ have a sample mean of 13.4
\item find a $98 \%$ confidence interval for the maximum value that $Y$ can take.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2018 Q6 [7]}}