| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2004 |
| Session | June |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Verify conditions in context |
| Difficulty | Moderate -0.8 This is a straightforward S2 binomial distribution question testing standard bookwork and routine calculations. Parts (a)-(e) involve stating conditions, identifying parameters, direct probability calculations using tables/calculator, and recalling mean/variance formulas. Part (f) requires a normal approximation with continuity correction, which is a standard S2 technique. All parts follow predictable patterns with no problem-solving or novel insight required, making this easier than average for A-level. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities5.02b Expectation and variance: discrete random variables5.04a Linear combinations: E(aX+bY), Var(aX+bY) |
\begin{enumerate}[label=(\alph*)]
\item State two conditions under which a random variable can be modelled by a binomial distribution. [2]
\end{enumerate}
In the production of a certain electronic component it is found that 10% are defective.
The component is produced in batches of 20.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Write down a suitable model for the distribution of defective components in a batch. [1]
\end{enumerate}
Find the probability that a batch contains
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item no defective components, [2]
\item more than 6 defective components. [2]
\item Find the mean and the variance of the defective components in a batch. [2]
\end{enumerate}
A supplier buys 100 components. The supplier will receive a refund if there are more than 15 defective components.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{5}
\item Using a suitable approximation, find the probability that the supplier will receive a refund. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2004 Q4 [13]}}