A distributor receives a large shipment of components. The distributor would like to accept the shipment if 10% or fewer of the components are defective and to return it if more than 10% of the components are defective. She decides to sample 10 components, and to return the shipment if more than 1 of the 10 is defective.

a. If the proportion of defectives in the batch is in fact 10%, what is the probability that she will return the shipment?

b. If the proportion of defectives in the batch is 20%, what is the probability that she will return the shipment?

c. If the proportion of defectives in the batch is 2%, what is the probability that she will return the shipment?

d. The distributor decides that she will accept the shipment only if none of the sampled items are defective. What is the minimum number of items she should sample if she wants to have a probability no greater than 0.01 of accepting the shipment if 20% of the components in the shipment are defective?