Flying Lukas needs to check in at Philadelphia Airport to take his US Airway flight to Boston. He can choose either to check in with a self-service counter or with an agent. During busy periods, a new passenger walks to a self-service counter every minute (with a standard deviation of 1 minute). The passengers who want to check in with an agent walk in every 5 minutes (with a standard deviation of 5 minutes). There are 5 self-service counters installed, while there are two agents. A typical check-in process takes 4 minutes (with a standard deviation of 4 minutes), regardless of whether an agent or a self-service counter is used. a. If Flying Lukas walks to a self-service counter to check in during a busy period, how long must he wait (on average) in line before he can use the machine? (Only include the waiting time, not any service time) b. If Flying Lukas goes to an agent, how long must he wait (on average) in line before being served? c. US Airways decides to have all check-ins be self-service. This would mean that the previous traffic of agent check-in passengers now flows to the self-service counters. What is the new average inter-arrival time at a self-service counter?