Question 26 An auditing software can identify 63.7% of misreporting issues in accounting iedgers. Let X be the number of accounting misreporting transactions identified by the software among 50 randomly selected transactions for the last 3 months. a) Determine the probability that no misreported transactions are found. [4 marks] b) Determine the probability that less than 10 misreported transactions are found. [4 marks] c) Determine the probability that at least half of the transactions are misreported. [6 marks] d) If the firm applying the auditing software as a test run finds no misreporting, it will receive a $200 compensation, but if there are less than 10 misreported transactions it will have to pay a fee of $50, and if the misreported transactions represent more than half of the transactions then the fee will be $100. Determine the expected monetary gain (assuming that the auditing software is correct when identifying a misreporting). [2+2+2=6 marks] [Total for Question 26 = 20 marks] Question 27 A new pipeline produced with recycled material on average has 3 faults that Eeak every 100 mts. The pipelines need to be repaired if 5 or less leaks are found, and the pipelines need to be replaced if 7 or more leaks are found. If the pipeline leaks are independent from each other: a) Determine the probability that no faulty leaks are found in a 100mts segment. [4 marks] b) Determine the probability that a pipeline segment needs repair. [6 marks] c) Determine the probabiiity that a pipelines segment needs repiacing. [6 marks] d) Find the expected number of 100mts segments that will need to be replaced for a 10,000mts pipeline. [4 marks] [Total for Question 27 = 20 marks]