| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2011 |
| Session | June |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Identify distribution and parameters |
| Difficulty | Easy -1.8 This is a very straightforward question requiring only identification of a sampling frame (list of identity numbers) and recognition that F follows B(50, 0.02). No calculations, no problem-solving—just direct recall and application of basic definitions from the specification. |
| Spec | 2.01a Population and sample: terminology5.02b Expectation and variance: discrete random variables5.02c Linear coding: effects on mean and variance5.02d Binomial: mean np and variance np(1-p) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| The list of ID numbers | B1 | For idea of list/register/database and identity numbers. NB B0 if referring to the sample or 50 or only part of the population |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(F \sim B(50, 0.02)\) | B1 B1 | 1st B1 for Binomial distribution; 2nd B1 for \(n=50\) and \(p=0.02\) or \((50, 0.02)\). NB \((0.02, 50)\) is B0. \(Po(1)\) alone is B0B0. For a probability table: 1st B1 use of \(B(50,0.02)\); 2nd B1 table must have all 50 values and their probabilities |
# Question 1:
## Part (a)
| Answer | Marks | Guidance |
|--------|-------|----------|
| The list of ID numbers | B1 | For idea of list/register/database and identity numbers. NB B0 if referring to the sample or 50 or only part of the population |
## Part (b)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $F \sim B(50, 0.02)$ | B1 B1 | 1st B1 for Binomial distribution; 2nd B1 for $n=50$ and $p=0.02$ or $(50, 0.02)$. NB $(0.02, 50)$ is B0. $Po(1)$ alone is B0B0. For a probability table: 1st B1 use of $B(50,0.02)$; 2nd B1 table must have all 50 values and their probabilities |
---\begin{enumerate}
\item A factory produces components. Each component has a unique identity number and it is assumed that $2 \%$ of the components are faulty. On a particular day, a quality control manager wishes to take a random sample of 50 components.\\
(a) Identify a sampling frame.
\end{enumerate}
The statistic $F$ represents the number of faulty components in the random sample of size 50.\\
(b) Specify the sampling distribution of $F$.\\
\hfill \mbox{\textit{Edexcel S2 2011 Q1 [3]}}