A bank has recently taken over the billing function of a company. An agreement stipulates that the bank should process 99.2% of the bills within 4 hours. A study of the current process indicates that the processing time averages 2.2 hours per bill with a standard deviation of 0.8 hours. A process improvement team has suggested a change. Experiments indicate that the change will lower the average processing time to 2 hours, but will raise the standard deviation to 1.2 hours.
a.) With the new system, what is the probability of processing the bills within 4 hours?
b.) With the current system, what is the probability of processing the bills within 4 hours?
c.) Should you change systems?