In a certain automobile manufacturing paint shop, paint defects on the hood occur at a mean rate of 0.8 defect per square meter. A hood on a certain car has an area of 3 square meters.
(a) Justify the use of the Poisson model.
(b) If a customer inspects a hood at random, what is the probability that there will be no defects?
(c) One defect?
(d) Fewer than two defects?