2 The number of telephone calls per day, \(X\), received by Candice may be modelled by a Poisson distribution with mean 3.5.
The number of e-mails per day, \(Y\), received by Candice may be modelled by a Poisson distribution with mean 6.0.
- For any particular day, find:
- \(\mathrm { P } ( X = 3 )\);
- \(\quad \mathrm { P } ( Y \geqslant 5 )\).
- Write down the distribution of \(T\), the total number of telephone calls and e-mails per day received by Candice.
- Determine \(\mathrm { P } ( 7 \leqslant T \leqslant 10 )\).
- Hence calculate the probability that, on each of three consecutive days, Candice will receive a total of at least 7 but at most 10 telephone calls and e-mails.
(2 marks)