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 $4$minutes$,$ and the arrival rate is $12$ per hour$($Poisson distributed$).$

Part $2$

$$a$)$ The average wait time in the line $=$

$$

enter your response here minutes $($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ The average number of customers waiting in the line $=$

$$

enter your response here customers $($round your response to three decimal$$ places$).$

Part $4$

$$c$)$ Mehmet raises the price to$$ $$5$ per cup and takes $60$seconds off the service time.$$ However, because the coffee is now so$$ expensive, the arrival rate drops to $9$ per hour.

Part $5$

The average wait time in the line $=$

$$

enter your response here minutes $($round your response to two decimal$$ places$).$

Part $6$

The average number of customers waiting in the line $=$

$$

enter your response here customers $($round your response to three decimal$$ places$).$