| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2010 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Identify distribution and parameters |
| Difficulty | Easy -1.2 This is a straightforward binomial distribution question requiring only recognition of the model (n=20, p=0.05) and direct application of standard formulas for P(X=0), P(X>4), mean, and variance. All parts are routine calculations with no problem-solving or conceptual challenges beyond basic S2 content. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(X \sim B(20, 0.05)\) | B1 B1 | (2 marks) |
| (b) \(P(X = 0) = 0.95^{20} = 0.3584859\ldots\) or \(0.3585\) using tables | M1 A1 | (2 marks) |
| (c) \(P(X > 4) = 1 - P(X \leq 4) = 1 - 0.9974 = 0.0026\) | M1 A1 | (2 marks) |
| (d) Mean \(= 20 \times 0.05 = 1\) | B1 | Variance \(= 20 \times 0.05 \times 0.95 = 0.95\) |
| Total [8] |
**(a)** $X \sim B(20, 0.05)$ | B1 B1 | (2 marks)
**(b)** $P(X = 0) = 0.95^{20} = 0.3584859\ldots$ or $0.3585$ using tables | M1 A1 | (2 marks)
**(c)** $P(X > 4) = 1 - P(X \leq 4) = 1 - 0.9974 = 0.0026$ | M1 A1 | (2 marks)
**(d)** Mean $= 20 \times 0.05 = 1$ | B1 | Variance $= 20 \times 0.05 \times 0.95 = 0.95$ | B1 | (2 marks)
| **Total [8]**
---\begin{enumerate}
\item A manufacturer supplies DVD players to retailers in batches of 20 . It has $5 \%$ of the players returned because they are faulty.\\
(a) Write down a suitable model for the distribution of the number of faulty DVD players in a batch.
\end{enumerate}
Find the probability that a batch contains\\
(b) no faulty DVD players,\\
(c) more than 4 faulty DVD players.\\
(d) Find the mean and variance of the number of faulty DVD players in a batch.\\
\hfill \mbox{\textit{Edexcel S2 2010 Q1 [8]}}