| Exam Board | AQA |
|---|---|
| Module | S2 (Statistics 2) |
| Year | 2013 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Continuous Uniform Random Variables |
| Type | Waiting time applications |
| Difficulty | Moderate -0.8 This is a straightforward application of continuous uniform distribution with clear context. Part (a) requires simple addition of minimum times (2+0+20+5=27), part (b) uses standard formulas for mean and variance of uniform distribution, and part (c) is a basic probability calculation. The question involves only routine recall and arithmetic with no problem-solving insight required. |
| Spec | 5.03a Continuous random variables: pdf and cdf5.03b Solve problems: using pdf5.03c Calculate mean/variance: by integration |
3 Mehreen lives a 2-minute walk away from a tram stop. Trams run every 10 minutes into the city centre, taking 20 minutes to get there. Every morning, Mehreen leaves her house, walks to the tram stop and catches the first tram that arrives. When she arrives at the city centre, she then has a 5-minute walk to her office.
The total time, $T$ minutes, for Mehreen's journey from house to office may be modelled by a rectangular distribution with probability density function
$$\mathrm { f } ( t ) = \begin{cases} 0.1 & a \leqslant t \leqslant b \\ 0 & \text { otherwise } \end{cases}$$
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Explain why $a = 27$.
\item State the value of $b$.
\end{enumerate}\item Find the values of $\mathrm { E } ( T )$ and $\operatorname { Var } ( T )$.
\item Find the probability that the time for Mehreen's journey is within 5 minutes of half an hour.
\end{enumerate}
\hfill \mbox{\textit{AQA S2 2013 Q3 [7]}}