| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2003 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | E(X) and Var(X) with probability calculations |
| Difficulty | Easy -1.3 This is a straightforward textbook exercise on binomial distribution requiring only direct application of standard formulas and definitions. Parts (a) and (d) are pure recall (stating X~B(4,0.3) and using E(X)=np, Var(X)=np(1-p)), part (b) is routine calculation and plotting, and part (c) requires identifying the mode. No problem-solving insight or multi-step reasoning is needed—just mechanical application of basic S2 content. |
| Spec | 2.04a Discrete probability distributions2.04b Binomial distribution: as model B(n,p)5.02b Expectation and variance: discrete random variables |
| Answer | Marks | Guidance |
|---|---|---|
| \(X \sim B(4, 0.3)\) | B1 B1 | (2) |
| Answer | Marks | Guidance |
|---|---|---|
| All probabilities correct | B1 | |
| Scales and labels | B1 | |
| Correct diagram | B1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| 1 resident | B1 | (1) |
| Answer | Marks | Guidance |
|---|---|---|
| \(E(X) = np = 1.2\) | B1 | |
| \(\text{Var}(X) = np(1-p)\) | ||
| \(= 4 \times 0.3 \times 0.7\) | M1 | |
| \(= 0.84\) | A1 | (3) |
## (a)
$X \sim B(4, 0.3)$ | B1 B1 | (2)
## (b)
All probabilities correct | B1 |
Scales and labels | B1 |
Correct diagram | B1 | (3)
## (c)
1 resident | B1 | (1)
## (d)
$E(X) = np = 1.2$ | B1 |
$\text{Var}(X) = np(1-p)$ |
$= 4 \times 0.3 \times 0.7$ | M1 |
$= 0.84$ | A1 | (3)
---In a town, 30\% of residents listen to the local radio station. Four residents are chosen at random.
\begin{enumerate}[label=(\alph*)]
\item State the distribution of the random variable $X$, the number of these four residents that listen to local radio. [2]
\item On graph paper, draw the probability distribution of $X$. [3]
\item Write down the most likely number of these four residents that listen to the local radio station. [1]
\item Find E($X$) and Var ($X$). [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2003 Q3 [9]}}