| Exam Board | SPS |
|---|---|
| Module | SPS SM Statistics (SPS SM Statistics) |
| Year | 2024 |
| Session | September |
| Marks | 10 |
| Topic | Binomial Distribution |
| Type | Independent binomial samples with compound probability |
| Difficulty | Moderate -0.3 This is a straightforward binomial distribution question requiring identification of the model (part i), a single probability calculation (part ii), and a two-stage binomial problem (part iii). While part (iii) requires recognizing a binomial-of-binomials structure, all techniques are standard A-level statistics with no novel insight needed. The multi-part structure and 10 marks suggest slightly below average difficulty overall. |
| Spec | 5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance |
At a factory that makes crockery the quality control department has found that 10\% of plates have minor faults. These are classed as 'seconds'. Plates are stored in batches of 12. The number of seconds in a batch is denoted by $X$.
\begin{enumerate}[label=(\roman*)]
\item State an appropriate distribution with which to model $X$. Give the value(s) of any parameter(s) and state any assumptions required for the model to be valid. [4]
\end{enumerate}
Assume now that your model is valid.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Find
\begin{enumerate}[label=(\alph*)]
\item P$(X = 3)$, [2]
\end{enumerate}
\item A random sample of 4 batches is selected. Find the probability that the number of these batches that contain at least 1 second is fewer than 3. [4]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Statistics 2024 Q5 [10]}}