Question $3$: $(35$ points$)$ The following data were collected during a delay study on a signalized intersection approach with tWO $/$aneS$.$ The cycle length of the signal is $60$ seconds.

a$)$ Estimate the time spent in queue for the average vehicle.

b$)$ Estimate the average control delay per vehicle on this approach.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$hline $\backslash$multirow$[$b$]\{2\}\{*\}\{$Check Time$\}$ & $\backslash$multirow$[$b$]\{2\}\{*\}\{$Cycle Number$\}$ & $\backslash$multicolumn$\{4\}\{|$c$|\}\{$Number of Vehicles in Queue$\}\backslash \backslash$

$\backslash$hline & & $0$ Sec & $15$ Sec & $30$ Sec & $45$ Sec $\backslash \backslash$

$\backslash$hline $9$:$00$ AM & $1$ & $3$ & $4$ & $2$ & $4\backslash \backslash$

$\backslash$hline $9$:$01$ AM & $2$ & $1$ & $2$ & $3$ & $3\backslash \backslash$

$\backslash$hline $9$:$02$ AM & $3$ & $4$ & $3$ & $3$ & $4\backslash \backslash$

$\backslash$hline $9$:$03$ AM & $4$ & $2$ & $3$ & $3$ & $4\backslash \backslash$

$\backslash$hline $9$:$04$ AM & $5$ & $0$ & $1$ & $2$ & $3\backslash \backslash$

$\backslash$hline $9$:$05$ AM & $6$ & $2$ & $1$ & $1$ & $2\backslash \backslash$

$\backslash$hline $9$:$06$ AM & $7$ & $4$ & $3$ & $3$ & $3\backslash \backslash$

$\backslash$hline $9$:$07$ AM & $8$ & $5$ & $5$ & $6$ & $4\backslash \backslash$

$\backslash$hline $9$:$08$ AM & $9$ & $2$ & $3$ & $4$ & $3\backslash \backslash$

$\backslash$hline $9$:$09$ AM & $10$ & $0$ & $3$ & $2$ & $2\backslash \backslash$

$\backslash$hline $9$:$10$ AM & $11$ & $1$ & $2$ & $3$ & $1\backslash \backslash$

$\backslash$hline $9$:$11$ AM & $12$ & $1$ & $0$ & $1$ & $0\backslash \backslash$

$\backslash$hline $9$:$12$ AM & $13$ & $2$ & $2$ & $1$ & $2\backslash \backslash$

$\backslash$hline $9$:$13$ AM & $14$ & $2$ & $3$ & $2$ & $2\backslash \backslash$

$\backslash$hline $9$:$14$ AM & $15$ & $4$ & $3$ & $3$ & $3\backslash \backslash$

$\backslash$hline $\backslash$multicolumn$\{6\}\{|$c$|\}\{\backslash ($ V$\_\{\backslash$text $\{$r $\}\}=435\backslash )$ vehs; $\backslash ($ V$\_\{\backslash$text $\{$srop $\}\}=305\backslash )$ vehs; FFS $\backslash (=35\backslash$mathrm$\{$mi$\}/\backslash$mathrm$\{$hr$\}\backslash )\}\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$