| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2008 |
| Session | June |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Probability of range of values |
| Difficulty | Moderate -0.8 This is a straightforward application of binomial distribution with standard calculations (cumulative probabilities, exact probabilities, mean/variance formulas). Part (c)(ii) requires basic interpretation comparing theoretical vs observed values, but no complex reasoning. All techniques are routine S1 material with no novel problem-solving required. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
6 For the adult population of the UK, 35 per cent of men and 29 per cent of women do not wear glasses or contact lenses.
\begin{enumerate}[label=(\alph*)]
\item Determine the probability that, in a random sample of 40 men:
\begin{enumerate}[label=(\roman*)]
\item at most 15 do not wear glasses or contact lenses;
\item more than 10 but fewer than 20 do not wear glasses or contact lenses.
\end{enumerate}\item Calculate the probability that, in a random sample of 10 women, exactly 3 do not wear glasses or contact lenses.
\item \begin{enumerate}[label=(\roman*)]
\item Calculate the mean and the variance for the number who do wear glasses or contact lenses in a random sample of 20 women.
\item The numbers wearing glasses or contact lenses in 10 groups, each of 20 women, had a mean of 16.5 and a variance of 2.50.
Comment on the claim that these 10 groups were not random samples.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S1 2008 Q6 [15]}}