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 $9000$ requires a constant $30$ 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 $55$ seconds. To help determine the amount of space needed for the line at the drive$-$up window, Burrito King would like to know the following:

a$.$ What is the average waiting line length $($in cars$)?$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Average line length

cars

b$.$ What is the average number of cars in the system $($both in line and at the window$)?$

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Average number of cars

cars

c$.$ What is the expected average time in the system, in minutes?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

Expected average time

minutes