| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2018 |
| Session | December |
| Marks | 9 |
| Topic | Approximating Binomial to Normal Distribution |
| Type | Probability between two values |
| Difficulty | Moderate -0.3 This is a standard Stats 1 normal approximation to binomial question with routine steps: identifying B(1000, 1/6), justifying normal approximation using np and nq criteria, applying continuity correction to find symmetric interval around the mean, then comparing with exact binomial probability. While it requires multiple techniques, all are textbook procedures with no novel problem-solving required, making it slightly easier than average. |
| Spec | 2.04b Binomial distribution: as model B(n,p)2.04d Normal approximation to binomial |
A fair dice is thrown 1000 times and the number, $X$, of throws on which the score is 6 is noted.
\begin{enumerate}[label=(\alph*)]
\item
\begin{enumerate}[label=(\roman*)]
\item State the distribution of $X$. [1]
\item Explain why a normal distribution would be an appropriate approximation to the distribution of $X$. [1]
\end{enumerate}
\item Use a normal distribution to find two positive integer values, $a$ and $b$, such that $\text{P}(a < X < b) \approx 0.4$. [5]
\item For your two values of $a$ and $b$, use the distribution of part (a)(i) to find the value of $\text{P}(a < X < b)$, correct to 3 significant figures. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2018 Q15 [9]}}