McGuckin Hardware in Boulder, Colorado, routinely receives shipments of 4 3 8 foot sheets of 1 2-inch-thick plywood. A plywood sheet may contain defects, for example, a knot, a split, or a deviation...

McGuckin Hardware in Boulder, Colorado, routinely receives shipments of 4 3 8 foot sheets of 1 2-inch-thick plywood. A plywood sheet may contain defects, for example, a knot, a split, or a deviation in wood structure. Defective sheets reduce profits because they are sold at a lower price. The manufacturer claims the proportion of all plywood sheets that are defective is 0.05. Suppose a large shipment of plywood sheets is received and 200 are randomly selected for inspection. If the sample proportion of defective sheets is more than 0.09, the entire shipment will be sent back to the supplier.

a. If the true proportion of defective plywood sheets is 0.05, what is the probability that the entire shipment will be sent back?

b. If the true proportion of defective plywood sheets is 0.03, what is the probability that the entire shipment will be sent back?

 c. If the true proportion of defective plywood sheets is 0.10, what is the probability that the shipment will be accepted?