You have just sent out a test mailing of a catalog to 1,000 people randomly selected from a database of 12,320 addresses. You will go ahead with the mass mailing to the remaining 11,320 addresses provided you receive orders from 2.7% or more from the test mailing within two weeks. Find the (approximate) probability that you will do the mass mailing under each of the following scenarios:
a. Assume that, in reality, exactly 2% of the population would send in an order within two weeks.
b. Assume that, in reality, exactly 3% of the population would send in an order within two weeks.
c. Assume that, in reality, exactly 4% of the population would send in an order within two weeks.