Answer to Question #205881 in Statistics and Probability for Lou Robert Cuyos

Question

What is the probability that the arrival time between consecutive customers is less than five minutes given that customers arrive at the claims counter at the rate of 15 per hour?

Answer 1

Time between arrivals is exponentially distributed with mean time beween arrivals of 4 minutes (15 per 0 minutes in average).

$$\dfrac{1}{\lambda}=4=>\lambda=0.25$$

$$P(X<5)=1-e^{-0.25(5)}\approx0.7135$$

The probability that the arrival time between consecutive customers is less than five minutes is 0.7135.