| Exam Board | Edexcel |
|---|---|
| Module | AEA (Advanced Extension Award) |
| Year | 2019 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Most likely value (mode) |
| Difficulty | Challenging +1.8 This AEA question requires understanding of binomial mode properties beyond standard A-level, including deriving the interval (n+1)p-1 < m ≤ (n+1)p and finding specific parameters where two modes exist (when (n+1)p is an integer). Part (c) demands systematic problem-solving with constraints, not just routine application. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
2.The discrete random variable $X$ follows the binomial distribution
$$X \sim \mathrm {~B} ( n , p )$$
where $0 < p < 1$ .The mode of $X$ is $m$ .
\begin{enumerate}[label=(\alph*)]
\item Write down,in terms of $m , n$ and $p$ ,an expression for $\mathrm { P } ( X = m )$
\item Determine,in terms of $n$ and $p$ ,an interval of width 1 ,in which $m$ lies.
\item Find a value of $n$ where $n > 100$ ,and a value of $p$ where $p < 0.2$ ,for which $X$ has two modes. For your chosen values of $n$ and $p$ ,state these two modes.
\end{enumerate}
\hfill \mbox{\textit{Edexcel AEA 2019 Q2 [8]}}