| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Independent binomial samples with compound probability |
| Difficulty | Moderate -0.3 This is a standard S2 binomial distribution question with routine applications: direct binomial probability calculations (parts a-b), binomial of binomials (part c), Poisson approximation (part d), and basic normal distribution (part e). All techniques are textbook exercises requiring no novel insight, though part (c) requires recognizing a second binomial layer and part (d) needs identifying the appropriate approximation, making it slightly easier than average overall. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities2.04d Normal approximation to binomial2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
A farmer noticed that some of the eggs laid by his hens had double yolks. He estimated the probability of this happening to be 0.05. Eggs are packed in boxes of 12.
Find the probability that in a box, the number of eggs with double yolks will be
\begin{enumerate}[label=(\alph*)]
\item exactly one, [3]
\item more than three. [2]
\end{enumerate}
A customer bought three boxes.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the probability that only 2 of the boxes contained exactly 1 egg with a double yolk. [3]
\end{enumerate}
The farmer delivered 10 boxes to a local shop.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Using a suitable approximation, find the probability that the delivery contained at least 9 eggs with double yolks. [4]
\end{enumerate}
The weight of an individual egg can be modelled by a normal distribution with mean 65 g and standard deviation 2.4 g.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{4}
\item Find the probability that a randomly chosen egg weighs more than 68 g. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 Q5 [15]}}