Empty buses arrive at a bus stop ever $45$ minutes.

Each bus has a capacity of $24$ passengers.

Passengers arrive at the stop one by one with

exponentially distributed interarrival times that

have a mean of $2\mathrm{.}5$ minutes. All passengers have

the same destination and get on the bus in a first$-$

come$-$first$-$serve fashion if there is a seat available.

A passenger takes $30$ seconds to get on the bus.

Once the buss is full or there are no more

passengers, the buss leaves immediately.

Any remaining passengers wait until the next bus.

Assuming that the first bus arrive $45$ minutes after the simulations starts, simulate

the bus stop for fifty replications where each replication is an $18-$hour day and

estimate:

$$ Average number of passengers on a bus.

$$ Average time a bus spends at the bus stop.

$$ Probability that a bus leaves the bus stop completely full