| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | E(X) and Var(X) with probability calculations |
| Difficulty | Easy -1.2 This is a straightforward binomial distribution question requiring only direct application of standard formulas and definitions. Students must identify X ~ B(4, 0.3), calculate probabilities using the binomial formula, plot them, identify the mode, and apply E(X) = np and Var(X) = np(1-p). All parts are routine recall with minimal problem-solving, making it easier than average for A-level. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities5.02d Binomial: mean np and variance np(1-p) |
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 Q3 [9]}}