A certain large shipment comes with a guarantee that it contains no more than 15% defective items. If the proportion of defective items in the shipment is greater than 15%, the shipment may be returned. You draw a random sample of 10 items. Let X be the number of defective items in the sample.
a. If in fact 15% of the items in the shipment are defective (so that the shipment is good, but just barely), what is P(X ≥ 7)?
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 P(X ≥ 2)?
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.