Statistical evaluation of a large sample justifies to model the number of cars which arrive daily for petrol between 12:00 a.m. and 4:00 a.m. at a particular filling station by a nonhomogeneous...

Statistical evaluation of a large sample justifies to model the number of cars which arrive daily for petrol between 12:00 a.m. and 4:00 a.m. at a particular filling station by a nonhomogeneous Poisson process {N(t), t ≥ 0} with intensity function

(1) How many cars arrive on average between 12:00 a.m. and 4:00 a.m.?

(2) What is the probability that at least 40 cars arrive between 2:00 and 4.00 a.m.?