Problem $18-2$

A vending machine dispenses hot chocolate or coffee. Service time is $30$ seconds per cup and is constant. Customers arrive at a mean rate of $80$ 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 $]$ customers

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

Average time $]$ minutes

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

Average number $$ customers