Statistics and Probability

A large shipment of computer chips 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, what is PiX 2 2)? b. Based on the answer to part (a), if 15% of the items in the shipment are defective, would 2 defectives in a sample of size 10 be an unusually large number? c. If you found that 2 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 PlX 2 7)? e. Based on the answer to part (d), if 15% of the items in the shipment are defective, would 7 defectives in a sample of size 10 be an unusually large number? 1'. If you found that 7 of the 10 sample items were defective, would this be convincing evidence that the shipment should be returned? Explain