Airgistics provides air consolidation and freight-forwarding services for companies that ship their products internationally. As a part of its commitment to continuous process improvement, Airgistics monitors the performance of its partner carriers to ensure that high standards of on-time delivery are met. Airgistics currently believes that it achieves a 96% on-time performance for its customers. Recently, a random sample of 200 customer shipments was selected for study, and 188 of them were found to have met the on-time delivery promise.
a. What is the probability that a random sample of 200 customer shipments would contain 188 or fewer on-time deliveries if the true population of on-time deliveries is 96%?
b. Would you be surprised if the random sample of 200 customer shipments had 197 on-time deliveries?
c. Suppose the random sample of 200 customer shipments revealed that 178 were on time. Would such a finding cause you to question Airgistics’s claim that its on-time performance is 96%? Support your answer with a probability calculation.