2020 jan question 5 f based on past historical trend 2 of a type of ch

Question

2020 Jan
Question 5
(f) Based on past historical trend, 2 % of a type of Christmas tree light bulbs are
defective. Assuming independence, the number of defective bulbs in a box of 100
bulbs follows a binomial model. Using the exact binomial distribution, the
probability that a box of 100 bulbs contains at most three defective bulbs is 0.859.
(i) If we use Poisson distribution as an approximation to binomial, determine
the mean of the Poisson model. Condition
(ii) It was found based on Poisson approximation, the probability that a box
of 100 bulbs contains at most three defective bulbs is 0.857.
Comment on the accuracy results obtained by the exact binomial model
as compared to the approximate Poisson model.