| Exam Board | WJEC |
|---|---|
| Module | Unit 4 (Unit 4) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Geometric applications |
| Difficulty | Standard +0.8 This question requires students to identify that θ is uniformly distributed on (0°, 90°), apply uniform distribution formulas for mean and variance, then crucially recognize that X = 8sin(θ) and solve P(8sin(θ) > 5) by finding the corresponding angle range. The transformation from uniform θ to the non-uniform distribution of X, combined with trigonometric manipulation, elevates this beyond standard uniform distribution exercises. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf |
2. The smallest angle $\theta$, in degrees, of a right-angled triangle with hypotenuse 8 cm , is uniformly distributed across all possible values.\\
\includegraphics[max width=\textwidth, alt={}, center]{8f47b2ff-f954-42ec-8ecc-fc64313a7b89-04_419_696_479_687}
\begin{enumerate}[label=(\alph*)]
\item Find the mean and standard deviation of $\theta$.
\item The shortest side of the triangle is of length $X \mathrm {~cm}$. Find the probability that $X$ is greater than 5 .
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 2024 Q2 [8]}}