call centres play an important

Question 5 (25 marks) Call centers play an important role in managing day-to-day business communications with customers. It is of vital importance to monitor a comprehensive set of service quality dimensions, which can help businesses understand the overall performance of a call center. One key dimension for measuring overall call center performance is service time which is defined as the time to answer an incoming call. Assume that the service time has a normal distribution. The data for time, in seconds, to answer 36 incoming calls to a financial services call center are 16 14 16 19 6 14 15 5 16 18 17 22 6 18 10 15 12 6 19 16 16 15 13 25 9 17 12 10 5 15 23 11 12 14 74 12 (a) At 0.05 level of significance, conduct a hypothesis test for whether there is evidence that the mean service time is less than 16 seconds? (11 marks) (b) The service performance is classified as excellent if the service time is less than 16 seconds. By stating the central limit theorem for sample proportion and verifying the conditions, find a 95% confidence interval for the proportion of excellent service performance. (9 marks) (c) Among the 36 incoming calls, 22 are related to financial charges. If 20 of the incoming calls are randomly chosen for a service quality research, find the probability that exactly 12 incoming calls are related to financial charges.