D. A shipment of 40,000 boxes of granola arrives at a distribution plant. It is understood that some boxes of granola will be defective, but if more than 1% of the boxes are defective, that is considered to be unacceptable, and the whole shipment should be returned. However, no one has time to check all 40,000 boxes of granola. So the granola quality control engineer will take a random sample of 400 boxes and will reject the entire shipment if 12 or more are defective.

Suppose that in fact 4% of the boxes in the entire shipment are defective. (The engineer doesn't know this.)

1. Should the engineer reject the shipment? (Base your answer on whatyouknow and the official policy of the distribution plant.)

2. What is the probability the engineer rejects the entire shipment?

3. If it were the case that just 0.8% of the boxes are defective, what would be the probability that the engineer would reject the shipment?

Before the engineer can put her plan into action, her manager stops her and makes her adopt a different strategy: to reject the shipment if the engineer takes a random sample of 400 boxes and more than 4 of the boxes are defective.

4. Using the manager's strategy, what is the probability the engineer rejects the entire shipment?

5. If it were the case that just 0.8% of the boxes are defective, what would be the probability that the engineer would reject the shipment, using the manager's strategy?