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 40 minutes and a standard deviation of 16 minutes.

i)Find the probability that a selected tax return will take more than 72 minutes to complete

Mr. Smith has just been approached by a small company for him to complete the taxreturns of all of their 15 employees within the next working day. Assuming that 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 15 employees is less than 8 hours?

Assume that 4% of the items produced in an assembly line operation are defective, but theproduction manager of the firm is not aware of this situation. A sample of parts are tested by the quality assurance department in order to determine the quality of the assembly operation and if the proportion of items found defective by the quality assurance test is 8% 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 125 parts, the assembly line will be shut down?