| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Normal approximation to binomial |
| Difficulty | Standard +0.3 This is a straightforward S2 binomial distribution question with standard probability calculations (parts a-b) and a routine normal approximation (part c). All techniques are textbook exercises: using binomial tables/formula for small n, applying normal approximation with continuity correction for large n, and stating the independence assumption. No novel insight or complex problem-solving required, making it slightly easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.04d Normal approximation to binomial |
A company always sends letters by second class post unless they are marked first class. Over a long period of time it has been established that 20\% of letters to be posted are marked first class.
In a random selection of 10 letters to be posted, find the probability that the number marked first class is
\begin{enumerate}[label=(\alph*)]
\item at least 3, [2]
\item fewer than 2. [2]
\end{enumerate}
One Monday morning there are only 12 first class stamps. Given that there are 70 letters to be posted that day,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item use a suitable approximation to find the probability that there are enough first class stamps, [7]
\item State an assumption about these 70 letters that is required in order to make the calculation in part (c) valid. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q4 [12]}}