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.

a. If in fact 15% of the items in the shipment are defective (so that the shipment is good, but just barely), what is the probability that 7 or more of the 10 sampled items are defective?

b. 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?

c. If you found that 7 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.

d. If in fact 15% of the items in the shipment are defective, what is the probability that 2 or more of the 10 sampled items are defective?

e. Based on the answer to part (d), if 15% of the items in the shipment are defective, would 2 defectives in a sample of size 10 be an unusually large number?

f. If you found that 2 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain.