| Exam Board | WJEC |
|---|---|
| Module | Unit 4 (Unit 4) |
| Year | 2018 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Waiting time applications |
| Difficulty | Standard +0.3 This is a straightforward continuous uniform distribution question requiring identification of U(0,12), recall of standard formulas for mean/variance, and basic probability calculations with conditional probability. The smartphone distraction adds a simple two-stage probability element but requires only routine application of probability rules without novel insight. |
| Spec | 2.04a Discrete probability distributions2.04e Normal distribution: as model N(mu, sigma^2) |
Antonio arrives at a train station at a random point in time. The trains to his desired destination are scheduled to depart at 12-minute intervals.
\begin{enumerate}[label=(\alph*)]
\item Assume that Antonio gets on the next train.
\begin{enumerate}[label=(\roman*)]
\item Suggest an appropriate distribution to model his waiting time and give the parameters.
\item State the mean and the variance of this distribution.
\item State an assumption you have made in suggesting this distribution. [4]
\end{enumerate}
\item Now assume that the probability that Antonio misses the next available train because he is distracted by his smartphone is $0 \cdot 12$. If he misses the next available train, he is sure to get on the one after that.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that he waits between 9 and 19 minutes.
\item Given that he waits between 9 and 19 minutes, find the probability that he gets on the first train. [6]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 4 2018 Q3 [10]}}