Question

Vehicles arriving at an intersection from one of the approach roads follow the poisson distribution. The mean rate of arrival is 900 vehicles per hour. If a gap is defined as the time difference between two successive vehicle arrivals (with vehicles assumed to be points), the probability (up to four decimal places) that the gap is greater than 8 seconds is

Answer 1

Answer:

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Answer 2

The gap greater than 8 seconds is 0.135

Mean rate of arrival = 900 (Given)

Time = 8 seconds (Given)

As per Poisson's Distribution -  

p ( h > 8 ) = e `8λ

λ = 900/ 36500

λ = 0.256

p ( h > 8 ) = e `81/4

= 0.1354

Thus, the gap greater than 8 seconds is 0.135