2 A new information technology centre is advertising places on its one-week residential computer courses.
\begin{enumerate}[label=(\alph*)]
\item The number of places, $X$, booked each week on the publishing course may be modelled by a Poisson distribution with a mean of 9.0.
\begin{enumerate}[label=(\roman*)]
\item State the standard deviation of $X$.
\item Calculate $\mathrm { P } ( 6 < X < 12 )$.
\end{enumerate}\item The number of places booked each week on the web design course may be modelled by a Poisson distribution with a mean of 2.5.
\begin{enumerate}[label=(\roman*)]
\item Write down the distribution for $T$, the total number of places booked each week on the publishing and web design courses.
\item Hence calculate the probability that, during a given week, a total of fewer than 2 places are booked.
\end{enumerate}\item The number of places booked on the database course during each of a random sample of 10 weeks is as follows:

$$\begin{array} { l l l l l l l l l l } 
14 & 15 & 8 & 16 & 18 & 4 & 10 & 12 & 15 & 8
\end{array}$$

By calculating appropriate numerical measures, state, with a reason, whether or not the Poisson distribution $\mathrm { Po } ( 12.0 )$ could provide a suitable model for the number of places booked each week on the database course.
\end{enumerate}

\hfill \mbox{\textit{AQA S2 2008 Q2 [11]}}