The time between arrivals of vehicles at a particular inters

The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 11 seconds.

What is the probability that the arrival time between vehicles is 12 seconds or less (to 4 decimals)?

What is the probability that the arrival time between vehicles is 6 seconds or less (to 4 decimals)?

What is the probability of 30 or more seconds between vehicle arrivals (to 4 decimals)?

Solution

The random variable follows a Exponential distribution with parameter l=1/11

a) probability that the arrival time between vehicles is 12 seconds or less=P( X<=12)=0.5756

use the excel function ==EXPONDIST(12,1/11,1)

b) probability that the arrival time between vehicles is 6 seconds or less =P(X<=6)=0.3486

c) probability of 30 or more seconds between vehicle arrivals=P( X >=30)=1-P(X<30)=0.1173