Kevin Murtuagh, manager of an national reservation service for a nationwide chain of luxury hotels, is concerned about productivity of his operation.  Analysis of recent historical data shows the call center seems to be averaging about five minutes to process a regular reservation call with a per call standard deviation of forty seconds. 

1. Suppose that every day Kevin randomly samples 25 calls for their length in minutes and computes the average.  Draw the x-bar process control chart with 3-sigma control limits.  On three consecutive days Kevin observes averages of 4.72, 5.20 and 5.03 minutes respectively.  Should he be concerned?  Explain.
2. Senior management has determined that call processing time should between 4 minutes, 15 seconds and 4 minutes, 45 seconds.  What is the probability that the current performance meets this standard? 
3. Given the information from senior management in part b, what is the current process capability?
4. Given your answer to part c, what should Kevin Murtaugh do in order to ensure that the process is 6-sigma qualified?  Explain.