2 A new information technology centre is advertising places on its one-week residential computer courses.
- 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.
- State the standard deviation of \(X\).
- Calculate \(\mathrm { P } ( 6 < X < 12 )\).
- 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.
- Write down the distribution for \(T\), the total number of places booked each week on the publishing and web design courses.
- Hence calculate the probability that, during a given week, a total of fewer than 2 places are booked.
- 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.