| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Central limit theorem |
| Type | Discrete uniform distribution sample mean |
| Difficulty | Moderate -0.3 This is a straightforward application of the central limit theorem with minimal complexity. Part (a) requires basic calculation of mean and variance for a discrete uniform distribution (routine formulas). Part (b) applies CLT directly to find P(X̄ < 3) using normal approximation—a standard textbook exercise with no conceptual challenges or multi-step reasoning beyond applying the formula for the sampling distribution of the mean. |
| Spec | 2.04a Discrete probability distributions2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation5.04a Linear combinations: E(aX+bY), Var(aX+bY)5.05a Sample mean distribution: central limit theorem |
A fair six-sided die is labelled with the numbers 1, 2, 3, 4, 5 and 6. The die is rolled 40 times and the score, $S$, for each roll is recorded.
\begin{enumerate}[label=(\alph*)]
\item Find the mean and the variance of $S$. [2]
\item Find an approximation for the probability that the mean of the 40 scores is less than 3 [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S3 2015 Q7 [5]}}