Statistical evaluation of a large sample justifies to model the number of cars which arrive daily for petrol between 0:00 and 4:00 a.m. at a particular filling station by an inhomogeneous Poisson process \(\{N(t), t \geq 0\}\) with intensity function

\[\lambda(t)=8-4 t+3 t^{2}\left[h^{-1}\right], \quad 0 \leq t \leq 4\]

(1) How many cars arrive on average between 0:00 and 4:00 a.m.?

(2) What is the probability that at least 40 cars arrive between 2:00 and 4:00?