| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Probability of range of values |
| Difficulty | Moderate -0.3 This is a straightforward binomial distribution question requiring standard cumulative probability calculations using tables or formulas. Part (a) involves routine P(X≤2), P(X≥2), and P(1<X<5) calculations with n=10, p=0.15. Part (b) extends to n=50 balls across 5 boxes but uses the same techniques. While multi-part with several calculations, it requires only direct application of binomial probability formulas without problem-solving insight, making it slightly easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
6 An amateur tennis club purchases tennis balls that have been used previously in professional tournaments.
The probability that each such ball fails a standard bounce test is 0.15 .
The club purchases boxes each containing 10 of these tennis balls. Assume that the 10 balls in any box represent a random sample.
\begin{enumerate}[label=(\alph*)]
\item Determine the probability that the number of balls in a box which fail the bounce test is:
\begin{enumerate}[label=(\roman*)]
\item at most 2 ;
\item at least 2;
\item more than 1 but fewer than 5 .
\end{enumerate}\item Determine the probability that, in $\mathbf { 5 }$ boxes, the total number of balls which fail the bounce test is:
\begin{enumerate}[label=(\roman*)]
\item more than 5 ;
\item at least 5 but at most 10 .
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{AQA S1 2011 Q6 [11]}}