| Exam Board | OCR |
|---|---|
| Module | H240/02 (Pure Mathematics and Statistics) |
| Year | 2017 |
| Session | Specimen |
| Marks | 6 |
| Topic | Normal Distribution |
| Type | Combined events across distributions |
| Difficulty | Moderate -0.8 Part (a) is a straightforward application of normal distribution and independence: find P(X < 194) using tables, then cube it. Part (b) requires reading a diagram to estimate standard deviation using the 68-95-99.7 rule or similar, which is routine but slightly less mechanical. Both parts are standard textbook exercises requiring only direct application of normal distribution properties with no problem-solving insight needed. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
\begin{enumerate}[label=(\alph*)]
\item The heights of English men aged 25 to 34 are normally distributed with mean 178 cm and standard deviation 8 cm.
Three English men aged 25 to 34 are chosen at random.
Find the probability that all three men have a height less than 194 cm. [3]
\item The diagram shows the distribution of heights of Scottish women aged 25 to 34.
\includegraphics{figure_7}
The distribution is approximately normal. Use the diagram in the Printed Answer Booklet to estimate the standard deviation of these heights, explaining your method. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR H240/02 2017 Q7 [6]}}