P $6\mathrm{.}5$ One$-$Box Models are Everywhere: Cars in a Parking Lot

In a downtown parking lot, $300$ cars enter per hour. Fifteen percent of them

immediately leave again, having found no free spot. The individual length of stay of parked cars varies. An observer notes that per minute, $1\%$ of the parked cars leave

the parking lot.

$($a$)$ How many parking spots does the parking lot have?

$($b$)$ How long does a car stay in the parking lot on average $($not counting the $15\%$

unsuccessful visitors$)?$

$($c$)$ Assume that the parking lot is open at $6$ A$.$M$.$ and is completely empty at that

time. The parking behavior remains exactly as previously described: $300$ cars enter

per hour $($of course, initially, all of them will find a free spot$),1\%$ parked cars leave

every minute. When is the parking lot full?