Question

A petrol station has two pumps. The service time follows the exponential distribution with mean 4 minutes and cars arrive for service in a Poisson process at the rate of 10 cars per hour. Find the probability that a customer has to wait for service. What proportion of time the pump remains idle?  

Answer 1

$\mu=\frac{60}{4}=15$

$\lambda=10$

$P(Customer has to wait for service)=\frac{1}{15-10}=0.2$

Proportion of time the pump stays idle = $\frac{10}{15}=0.66$