Question 2 ([2 + 2] + 2 = 6 marks) a) Mr Smith is a local tax agent with 20 years of experience. He knows that the time taken to complete a single tax return is normally distributed with a mean of 30 minutes and a standard deviation of 12 minutes. 0 Find the probability that a selected tax return will take more than 50 minutes to complete ii) Mr. Smith has just been approached by a small company for him to complete the tax Mr. Smith works 8 hours a day, what is the probability that the total time it takes Mr. Smith to complete all the tax returns for the 20 employees is less than 8 hours? b} Assume that 5% of the items produced in an assembly line operation are defective, but the production manager of the firm is not aware of this situation. A sample of parts are tested by the quality assurance department in_9rler_39_ determine the quality of the assembly operation and if the proportion of items found defective by the quality assurance test is 10% or more, the assembly line operation will be shut down to check for the cause of the defects. What is the probability that in a sample of 150 parts, the assembly line will be shut down