| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Overbooking probability problems |
| Difficulty | Moderate -0.8 This is a straightforward application of binomial-to-normal approximation with continuity correction. Part (a) requires identifying X ~ B(200, 0.03) for no-shows, parts (b) and (c) involve routine normal approximation calculations with clearly defined boundaries. The question is easier than average because it explicitly tells students to use an approximation, requires minimal setup, and involves standard probability calculations without conceptual challenges. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04d Normal approximation to binomial |
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. [2]
\end{enumerate}
By using a suitable approximation, find the probability that
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item more than 196 passengers turn up for this flight, [3]
\item there is at least one empty seat on this flight. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q3 [7]}}