Really need help with this question!

Question

1.a company manufactures batteries in batches of 18 and there is a

3 percent defect rate

why is this a binomial distribution please explain!

Answer 1

Here is why:

(1) In each batch of 18 batteries produced, a battery is either defective or nondefective

(2) There is a 3% defective rate which stays the same for each batch of 18 batteries produced. That is, the probability/likelihood of a battery being defective is 0.03 and this probability does not change from batch to batch

(3) Each batch of manufacture is independent of the other.

Now define a random variable X = the number of defective batteries manufactured in a batch of 18. Then X has a binomial distribution with n = 18 and probability of defect, p = 0.03