An automobile manufacturer finds that 1 in every 2000 automobiles produced has a particular manufacturing defect.

(a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 5000 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p. Repeat(a) using a Poisson distribution and compare the results.

(a) The probability using the binomial distribution is

nothing

.

(Round to five decimal places asneeded.)