Problem $10-7($Algo$)$

Burrito King $($a new fast$-$food franchise opening up nationwide$)$ has successfully automated burrito production for its drive$-$up fast$-$food establishments. The Burro$-$Master $9,000$ requires a constant $50$ seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive$-$up window according to a Poisson distribution at an average of one every $65$ seconds.

a$.$ What is the average waiting line length $($in cars$)?($Do not round intermediate calculations. Round your answer to $\backslash (\backslash$mathbf$\{2\}\backslash )$ decimal places.$)$

Average line length

b$.$ What is the average number of cars in the system $($both in line and at the window$)?($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Average number of cars

c$.$ What is the expected average time in the system, in minutes? $($Do not round intermediate calculations. Round your answer to $2$ decimal places.$)$

Expected average time