When customers of Henniker Bank believe a mistake has been made on their account statements, their claims are forwarded to the bank’s research department, whose trained clerks carefully research and document the transactions in question. On completing her investigation, a clerk phones the customer with her findings. The research department has three clerks. Each handles claims from a separate geographic district and never works on claims from outside her own district. The average number of complaints arising from each district is the same, 3.5 per week. The clerks are equally experienced and completely process the average claim in 1.2 days. Assume a five- day week.
a. Across all districts, how many claims are waiting to be processed on average? What fraction of claims is completed in less than 10 business days?
b. The bank is considering introducing a new information system that would reduce the standard deviation of the service distribution by 50%, although the mean would remain unchanged. How would your answers to part a change?