7 Items from a production line are examined for any defects. The probability that any item will be found to be defective is 0.15 , independently of all other items.
- A batch of 16 items is inspected. Using tables of cumulative binomial probabilities, or otherwise, find the probability that
(a) at least 4 items in the batch are defective,
(b) exactly 4 items in the batch are defective. - Five batches, each containing 16 items, are taken.
(a) Find the probability that at most 2 of these 5 batches contain at least 4 defective items.
(b) Find the expected number of batches that contain at least 4 defective items.