Here is one popular method of acceptance sampling: a sample of n items is randomly selected with replacement and the entire batch is rejected if there is at least one defect. SPRI Corporation has just manufactured 100,000 DVDs, and 1% are defective. A buyer is committed to buy the whole batch of 100,000 DVDs from SPRI Corporation. The only way the buyer can get out of the contract is if a random sample of 15 DVDs is selected and at least one is defective.
a) What is the probability that the buyer will end up not purchasing the whole batch of 100,000 DVDs?
b) If you want to reduce the probability in part a) to 5% by doing better quality control in the manufacturing process, how low a defective rate do you have to reduce to in order that the whole batch will be sold with 95% probability?