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.