S2 January 2007 Q2
2. The random variable \(J\) has a Poisson distribution with mean 4.
(a) Find \(\mathrm{P}(J \geqslant 10)\). (2)
The random variable \(K\) has a binomial distribution with parameters \(n = 25\), \(p = 0.27\).
(b) Find \(\mathrm{P}(K \leqslant 1)\). (3)
| Scheme | Marks |
|---|---|
| \(\mathrm{P}(J \geqslant 10) = 1 - \mathrm{P}(J \leqslant 9) \quad\) or \(= 1 - \mathrm{P}(J \lt 10)\) | M1 |
| \(= 1 - 0.9919\) \(= 0.0081\) | A1 |
| (2) |
Notes
M1 \(1 - 0.9919\) implies method
A1 awrt 0.0081
| Scheme | Marks |
|---|---|
| \(\mathrm{P}(K \leqslant 1) = \mathrm{P}(K = 0) + \mathrm{P}(K = 1)\) | M1 |
| \(= (0.73)^{25} + 25(0.73)^{24}(0.27)\) | M1 |
| \(= 0.00392\) | A1 |
| (3) | |
| (5 marks) |
Notes
1st M1 both, implied below even with ‘25’ missing
2nd M1 clear attempt at ‘25’ required
A1 awrt 0.0039 implies M