Question

Traffic on a highway is moving at a rate 360 vehicles per hour at a location. If the number of vehicles arriving on this highway follows Poisson distribution, the probability (round off to 2 decimal places) that the headway between successive vehicles lies between successive vehicles lies between 6 and 10 seconds in

• A. 0.18

Answer 1

The correct option is A 0.18

$\lambda =360veh/hr$
$=\frac{360}{3600}.\frac{veh}{sec}=0.1veh/sec$
$P\left(6\to 10\right)=\frac{{\left({\mathrm{\lambda t}}_2\right)}^0{e}^{-{\mathrm{\lambda t}}_2}}{0!}-\frac{{\left({\mathrm{\lambda t}}_1\right)}^0{e}^{-{\mathrm{\lambda t}}_1}}{0!}$
=$\frac{1\times e^{-0.1\times 6}}{1}-\frac{1\times e^{-0.1\times 10}}{1}$
=0.18