An observer counts 220 veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed,the probability of having five vehicles arriving over a 38 sec time interval is

0.025

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0.065

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0.075

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0.055

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Solution

The correct option is D 0.055
$P = \frac{(λ t)^{n} e^{- λ t}}{n!}$
$λ = 220 v e h / h r, t = 38 s e c, n = 5$
$P = \frac{{(220 \times \frac{38}{3600})}^{5} \times e^{- 220 \times \frac{38}{3600}}}{5 \times 4 \times 3 \times 2 \times 1} = 0.055$

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An observer counts 220 veh/h at a specific highway location. Assume that the vehicle arrival at the location is Poisson distributed,the probability of having five vehicles arriving over a 38 sec time interval is

The correct option is D 0.055P=(λt)ne−λtn! λ=220veh/hr,t=38sec,n=5 P=(220×383600)5×e−220×3836005×4×3×2×1=0.055

The correct option is D 0.055
$P = \frac{(λ t)^{n} e^{- λ t}}{n!}$
$λ = 220 v e h / h r, t = 38 s e c, n = 5$
$P = \frac{{(220 \times \frac{38}{3600})}^{5} \times e^{- 220 \times \frac{38}{3600}}}{5 \times 4 \times 3 \times 2 \times 1} = 0.055$