Traffic flow data were collected using a loop detector embedded in a lane of a highway. During a $15-$second period, the detector recorded the passage of $6$ vehicles and their brief durations appeared over the detector are $0\mathrm{.}23,0\mathrm{.}27,0\mathrm{.}25,0\mathrm{.}24,0\mathrm{.}26,$ and $0\mathrm{.}22$ second, respectively. Assume detector width $6ft$ and average vehicle length $18ft.$ Find: $(1).$ Flow rate, $(2).$ Time$-$mean speed, $(3).$ Occupancy, and $(4).$ Traffic density.