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A corporation has 11 manufacturing plants. Of these, seven are domestic and four are located outside the United States. Each year, a performance evaluation is conducted for 4 randomly selected plants.
a. What is the probability that a performance evaluation will include exactly 1 plant outside the United States?
b. What is the probability that a performance evaluation will contain 3 plants from the United States?
c. What is the probability that a performance evaluation will include 2 or more plants from outside the United States?
A new phone-answering system installed by the Ohio Power Company is capable of handling five calls every 10 minutes. Prior to installing the new system, company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to two every 10 minutes. If this incoming call distribution is what the analysts think it is, what is the probability that in a 10-minute period more calls will arrive than the system can handle? Based on this probability, comment on the adequacy of the new answering system.