A certain large shipment comes with a guarantee that it contains no more than defective items. If the proportion of defective items in the shipment is greater than , the shipment may be returned. You draw a random sample of items. Let be the number of defective items in the sample. a)If in fact of the items in the shipment are defective. Find .
[7 marks]
b)Based on the answer to 2(a), if of the items in the shipment are defective, would defectives in a sample of size 10 be an unusually large number?
[8 marks]
c)If you found that of the sample items were defective, would this be convincing evidence that the shipment should be returned? Explain. [10marks]