Altug's Coffee Shop decides to install an automatic coffee vending machine outside one of its stores to reduce the number of people standing in line inside. Mehmet Altug charges $$3\mathrm{.}50$ per cup. However, it takes too long for people to make change. The service time is a constant $1\mathrm{.}50$ minutes, and the arrival rate is $30$ per hour $($Poisson distributed$).$

a$)$ The average wait time in the line $=$ minutes $($round your response to two decimal places$).$

b$)$ The average number of customers waiting in the line $=,$ customers $($round your response to three decimal places$).$

c$)$ Mehmet raises the price to $$5$ per cup and takes $30$ seconds off the service time. However, because the coffee is now so expensive, the arrival rate drops to $24$ per hour.

The average wait time in the line $=,$ minutes $($round your response to two decimal places$).$

The average number of customers waiting in the line $=,$ customers $($round your response to three decimal places$).$