1. A store employs one cashier at its counter. Nine customers arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes.

1) Average number of customers in the system.

2) Average number of customers in the queue

3) Average time a customer spends in the system.

4) Average time a customer waits before being served.

2. a) Speeds on a roadway are uniformly distributed between 80 km/hr and 130 km/hr. If one of these speeds is selected at random, what is the probability that it will be between 99 km/hr and 111 km/hr?

(b) Timesspent waiting for the next event are distributed exponentially according to e t where t is in minutes. Find the probability of waiting less than 30 seconds for the next event.