QUESTION $3(17\mathrm{.}5$ marks$)$

Uniport Ventures operates an automatic car wash at Delta Park for Senior Staff of the University who patronise the Senior Staff Club. Cars arrive at a poisson distribution rate of $8$ per hour. The automated car wash takes exactly five minutes. Calculate: $($i$)$ The average number of cars waiting in line for a wash $(7\mathrm{.}5$ marks$).($ii$)$ The avarage time that cars spend at the car wash $(7\mathrm{.}5$ marks$)($iii$)$ The capacity utilisation of the business. $(2\mathrm{.}5$marks$)$