1 At a certain location on Eskisehir road the number of cars

1. At a certain location on Eskisehir road, the number of cars exceeding the speed limit by more than 10 kilometres per hour, during a half hour period is a Poisson random variable with mean of 8.4 per half hour. What is the probability that waiting time for the second car exceeding the speed limit by more than 10 kilometres per hour, will be less than 5 minutes.

Solution

T =waiting time for the second car exceeding the speed limit by more than 10 kms per hour....
5 minutes= 0.1666667 half hour...

prob( T < 0.1666667 ) = 1 - e^ - (0.1666667 * 8.4 ) = 0.7534031