Question

Vehicles arrive at an intersection at a rate of 400 veh/h according to a Poisson distribution. What is the probability that more than five vehicles will arrive in a one-minute interval?

Answer 1

0.6547 or 65.47%

Explanation:

One minute equals 1/60 of an hour, the mean number of occurrences in that interval is:

`\lambda =(400)/(60)=6.6667`

The poisson distribution is described by the following equation:

`P(x) =(\lambda^(x)*e^(-\lambda))/(x!)`

The probability that more than 5 vehicles will arrive is:

`P(x>5)= 1-(P(0)+P(1)+P(2)+P(3)+P(4)+P(5))\\P(x>5) = 1-((6.667^(0)*e^(-6.667))/(1)+(6.667^(1)*e^(-6.667))/(1)+(6.667^(2)*e^(-6.667))/(2)+(6.667^(3)*e^(-6.667))/(3*2)+(6.667^(4)*e^(-6.667))/(4*3*2)+(6.667^(5)*e^(-6.667))/(5*4*3*2))\\P(x>5)=1-(0.00127+0.00848+0.02827+ 0.06283+0.10473+0.13965)\\P(x>5)=0.6547`

The probability that more than five vehicles will arrive in a one-minute interval is 0.6547 or 65.47%.