Question

2. A manufacturer of big screen smart TVs ships them in lots of 1000 TVs per lot. Before shipment, 30 TVs are randomly selected from each lot and tested. If none is defective, the lot is shipped. It is known that each TV has a probability of 0.005 of being defective independent of each other TV.

A. What is the exact distribution of X, the number of defective TVs in the 30 sampled TVs?

B. Find the exact probability of shipping a lot.

C. Approximate the probability in B using the appropriate distribution. Justify your answer

Answer 1

c. Binomial distribution is approximated by normal distribution.

But for this two conditions need to be satisfied

1. np 10

2. nq 10

Here np = 0.15 and nq = 29.85,  condition 1 is not satisfied. Hence we can not use approximation to this binomial distribution.