| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Probability of range of values |
| Difficulty | Easy -1.2 This is a straightforward binomial distribution question requiring only basic probability concepts. Students must identify parameters (n=20, p=1/3), write the standard binomial probability formula, state the domain, and perform a calculator computation. All steps are routine A-level statistics with no problem-solving or novel insight required. |
| Spec | 2.04f Find normal probabilities: Z transformation2.05e Hypothesis test for normal mean: known variance |
A school contains 500 students in years 7 to 11 and 250 students in years 12 and 13. A random sample of 20 students is selected to represent the school at a parents' evening. The number of students in the sample who are from years 12 and 13 is denoted by $X$.
\begin{enumerate}[label=(\alph*)]
\item State a suitable binomial model for $X$. [1]
\end{enumerate}
Use your model to answer the following.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item \begin{enumerate}[label=(\roman*)]
\item Write down an expression for $\text{P}(X = x)$. [1]
\item State, in set notation, the values of $x$ for which your expression is valid. [1]
\end{enumerate}
\item Find $\text{P}(5 \leqslant X \leqslant 9)$. [2]
\item State one disadvantage of using a random sample in this context. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2023 Q9 [6]}}