$15$

$4.$ The traffic flow on a highway is composed of free flowing and restrained vehicles. The free flowing vehicles have a mean headway of $6\mathrm{.}0$ secs$,$ while the restrained vehicles do not approach closer to one another than the time headway of $0\mathrm{.}5s.$ When the traffic volume was $1000ve\frac{h}{h},$ it was noted that there were $25\%$ free flowing and the rest are restrained type. Calculate: i$)$ The proportion of vehicles with a time headway greater than $6$ seconds, ii$)$ the time headway at which only $5\%$ of vehicles are restrained, iii$)$ the proportion of restrained vehicles which have a headway greater than $0\mathrm{.}25s.$

$(5)$