An observer counts 240 veh/h at a specific highway location. Assume that the vehicles arrival at the location is Poisson distributed, the probability of having one vehicle arriving over a 30-second time interval is _______.

0.27

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Solution

The correct option is A 0.27
Let X ={No. of vehicles per 30 sec time interval}

So average number of vehicles $(λ) = 240 veh/hour$

$= \frac{240}{60} veh/min$

= 4 veh/min = 2 veh/30 sec.

The required probability is P(X = 1)

$= \frac{e^{- λ} . λ^{1}}{1!} = e^{- 2} .2 = 0.27$

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An observer counts 240 veh/h at a specific highway location. Assume that the vehicles arrival at the location is Poisson distributed, the probability of having one vehicle arriving over a 30-second time interval is _______. 0.27

The correct option is A 0.27Let X ={No. of vehicles per 30 sec time interval} So average number of vehicles(λ)=240 veh/hour =24060 veh/min = 4 veh/min = 2 veh/30 sec. The required probability is P(X = 1) =e−λ.λ11!=e−2.2=0.27

An observer counts 240 veh/h at a specific highway location. Assume that the vehicles arrival at the location is Poisson distributed, the probability of having one vehicle arriving over a 30-second time interval is _______.

0.27

The correct option is A 0.27
Let X ={No. of vehicles per 30 sec time interval}

So average number of vehicles $(λ) = 240 veh/hour$

$= \frac{240}{60} veh/min$

= 4 veh/min = 2 veh/30 sec.

The required probability is P(X = 1)

$= \frac{e^{- λ} . λ^{1}}{1!} = e^{- 2} .2 = 0.27$