Chapter 6.2, Problem 41E

Testing a shipment: A certain large shipment comes with a guarantee that it contains no more than 15% defective items. If the proportion of items in the shipment is greater than 15%, the shipment may be returned. You draw a random sample of 10 items and test each one to determine whether it is defective.

1. If in fact 15% of the items in the shipment are defective (so that the is good, but just barely), what is the that 7 or more of the 10 sampled items are defective?
2. Based on the answer to part (a), if 15% of the items in the shipment are defective, would 7 defectives in a sample of size 10 be an unusually large number?
3. If you found that 7 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.
4. If in fact 15% of the items in die shipment are defective, what is the probability that 2 or more of the 10 sampled items are defective?
5. Based on the answer to part (d), 15% of the items in the are defective, would 2 defectives a sample of size 10 be an unusually large number?
6. If you found that 2 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.