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...

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.