| Exam Board | Edexcel |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2004 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Probability between two values |
| Difficulty | Moderate -0.3 Part (a) and (b) are pure recall (p=0.5 for symmetry), worth 2 marks. Part (c) is a standard S2 application: calculate mean/variance, apply continuity correction, and use normal tables. This is a textbook exercise with no problem-solving required, making it slightly easier than average despite the 7-mark calculation component. |
| Spec | 2.04d Normal approximation to binomial2.04f Find normal probabilities: Z transformation5.04b Linear combinations: of normal distributions |
The discrete random variable $X$ is distributed B($n$, $p$).
\begin{enumerate}[label=(\alph*)]
\item Write down the value of $p$ that will give the most accurate estimate when approximating the binomial distribution by a normal distribution. [1]
\item Give a reason to support your value. [1]
\item Given that $n = 200$ and $p = 0.48$, find P($90 \leq X < 105$). [7]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S2 2004 Q3 [9]}}