In python develop a computer simulation based on the provided information and run it many times.

Collect simulation output data to determine the distribution of the following metrics:

$$ The average wait time for a worker.

$$ The average number of people that walk to the $2$nd$,3$rd$,$ and $4$th floors on a given day.

$$ The time that the last worker boards the elevator each day.

$$ The average number of workers in line at $8$:$30,8$:$45,$ and $9$:$00$ each day.