| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2025 |
| Session | April |
| Marks | 11 |
| Topic | Binomial Distribution |
| Type | Independent binomial samples with compound probability |
| Difficulty | Moderate -0.8 This is a straightforward binomial distribution question requiring standard identification of model and parameters, direct probability calculations using given formulas or tables, and a simple extension to a binomial-of-binomial scenario. All parts follow textbook templates with no novel problem-solving required, making it easier than average A-level questions. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
A retail bakery makes cherry muffins where, due to the production process, 15% of muffins contain a lower than expected quantity of cherries. The bakery sells these muffins in boxes of 20.
\begin{enumerate}[label=(\alph*)]
\item State a suitable distribution to model the number of muffins with a lower than expected quantity of cherries in a box, giving the value(s) of any parameter(s). State any assumptions needed for your model to be valid. [4]
\item Using your model from part (a), find the probability that a randomly selected box contains:
\begin{enumerate}[label=(\roman*)]
\item exactly 3 muffins with a lower than expected quantity of cherries, [2]
\item at least 5 muffins with a lower than expected quantity of cherries. [2]
\end{enumerate}
\item The bakery sells 25 boxes of muffins in one day. Find the probability that fewer than 4 of these boxes contain exactly 3 muffins with a lower than expected quantity of cherries. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2025 Q6 [11]}}