| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Normal distribution parameters found then approximation applied |
| Difficulty | Standard +0.3 This is a straightforward S2 question testing standard normal distribution and binomial-to-normal approximation. Part (a) requires inverse normal calculation (routine), part (b) is direct binomial probability, and part (c) applies the standard continuity correction formula. All techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04d Normal approximation to binomial2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
A garden centre sells canes of nominal length 150 cm. The canes are bought from a supplier who uses a machine to cut canes of length L where L ~ N($\mu$, 0.3²).
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\mu$, to the nearest 0.1 cm, such that there is only a 5\% chance that a cane supplied to the garden centre will have length less than 150 cm. [4]
\end{enumerate}
A customer buys 10 of these canes from the garden centre.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the probability that at most 2 of the canes have length less than 150 cm. [3]
\end{enumerate}
Another customer buys 500 canes.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Using a suitable approximation, find the probability that fewer than 35 of the canes will have length less than 150 cm. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q5 [13]}}