Chrystabs Coffee Shop has decided to install an automatic coffee vending machine outside one of its stores to reduce the number of people standing in line inside. Chrystab charges $$3\mathrm{.}50$ per cup. However, it takes too long for people to make change. The service time is a constant $3$ minutes, and the arrival rate is $15$ per hour $($Poisson distributed$).$a$)$What is the average wait in line?b$)$What is the average number of people in line?c$)$Chrystab raises the price to $$5$ per cup and takes $60$ seconds off the service time. However, because the coffee is now so expensive, the arrival rate drops to $10$ per hour. Now what are the average wait time and the average number of people in the queue $($waiting$)?$