| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2002 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Overbooking probability problems |
| Difficulty | Moderate -0.3 This is a standard S2 textbook exercise requiring identification of a binomial model and normal approximation with continuity correction. The setup is straightforward (n=200, p=0.97), and parts (b) and (c) involve routine probability calculations using tables. While it requires multiple steps, each follows a well-practiced procedure with no novel insight needed. |
| Spec | 2.04d Normal approximation to binomial5.02b Expectation and variance: discrete random variables5.04b Linear combinations: of normal distributions |
3. An airline knows that overall $3 \%$ of passengers do not turn up for flights. The airline decides to adopt a policy of selling more tickets than there are seats on a flight. For an aircraft with 196 seats, the airline sold 200 tickets for a particular flight.
\begin{enumerate}[label=(\alph*)]
\item Write down a suitable model for the number of passengers who do not turn up for this flight after buying a ticket.
By using a suitable approximation, find the probability that
\item more than 196 passengers turn up for this flight,
\item there is at least one empty seat on this flight.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2002 Q3 [7]}}