In the Leo Company, 18,000 checks were issued during a designated period of time. Concern exists within management that some of these checks may be forgeries. As part of your regular audit engagement, you agree to use discovery sampling to test for such occurrences.

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a. Assuming you desire 95 percent probability of detecting at least one occurrence, determine sample size when the critical number of occurrences is (1) 54 , (2) 90 , and (3) 180.

b. Assuming no occurrences are found in the above samples, what is the probability that the number of occurrences is less than 18 in (1), less than 54 in (2), and less than 90 in (3)?

c. Assuming 3 occurrences were found in a discovery sample designed to provide a 95 percent probability of detecting one occurrence when the critical number of occurrences was 180, what is the upper precision limit on the occurrence of forgeries?