Manufacturing and Product Development
In early 2013 there was a worldwide glut of solar panels. This forced prices down and made this form of energy production affordable to many more people. This oversupply of solar panels may have caused some manufacturers to cut corners. Sainty Solar is a leading producer and claims the proportion of its solar panels that are defective is 0.02. Solar Solutions, a leading installer, receives a shipment of 50,000 solar panels. Before accepting the entire lot, Solar Solutions selects a random sample of 25 panels and thoroughly tests each one. If four or more panels are found to be defective, the entire shipment will be sent back. Otherwise the shipment will be accepted.
a. Suppose the claim is true: The actual proportion of defectives is p 5 0.02. What is the probability that the shipment will be rejected? (This is one type of error probability. The company would be making a mistake if this event occurred. It would be rejecting the shipment when the proportion of defectives is as claimed.)
b. Suppose the actual proportion of defectives is p = 0.05. What is the probability that the shipment will be accepted? (This is another type of error probability. In this case, the company would also be making a mistake. It would be accepting the shipment when the proportion of defectives is too high.)
c. Suppose the actual proportion of defectives is p = 0.07. What is the probability that the shipment will be accepted?