Question

A company purchases shipments of batteries and uses this acceptance sampling plan:  Randomly select and test 40 batteries.  Accept the batch if there are fewer than 3 defects.  A particular shipment of thousands of batteries has a 3.2% rate of defects. Below, we will find the probability that the whole shipment will be accepted.

A) How do we know that this problem is a binomial problem?  Explain your answer in one or two sentences. (Hint: Do we have independent trials?  Do we have two conditions, success and failure? Do we meet the sample size requirement, etc.?)

B) What would you consider the condition of “success” in this binomial problem? Would it be considered “success” in real life? Justify your answer in at least two sentences. (Hint: Think about the probability you will use to solve the problem. With what condition is it associated? “Success” in binomial probability is not always “success” in real life!)

Answer 1

(A) Yes, the trials are independent because one battery being defective does not affect another battery being good or defective. We have two conditions: a battery being defective (success) and a battery being not defective (failure). The sample size requirement is met because we are sampling only 40 batteries where the company is producing thousands of batteries.

(B) In this problem a "success" is defined as a battery being defective. This is not so in real life. In real life we would rather call finding a good battery as a "success". So, "success" in a binomial experiment is not always a "success" in real life.