A vending machine dispenses hot chocolate or coffee. Service time is $15$ seconds per cup and is rate of $55$ per hour, and this rate is Poisson$-$distributed.

a$.$ Determine the average number of customers waiting in line. $($Round your answer to $2$ decimal places.$)$

Average number of customer

b$.$ Determine the average time customers spend in the system. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Average time minutes

c$.$ Determine the average number of customers in the system. $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Average number

customers