4 A multi-storey car park has two entrances and one exit. During a morning period the numbers of cars using the two entrances are independent Poisson variables with means 2.3 and 3.2 per minute. The number leaving is an independent Poisson variable with mean 1.8 per minute. For a randomly chosen 10-minute period the total number of cars that enter and the number of cars that leave are denoted by the random variables \(X\) and \(Y\) respectively.

1. Use a suitable approximation to calculate \(\mathrm { P } ( X \geqslant 40 )\).
2. Calculate \(\mathrm { E } ( X - Y )\) and \(\operatorname { Var } ( X - Y )\).
3. State, giving a reason, whether \(X - Y\) has a Poisson distribution.