An installation technician for specialized communication system is dispatched to city only when three or more orders have been placed. Assume orders follow Poisson distribution with mean of 0.25 per week for city with population of 100,000, and assume your city contains a population of 800,000.
a. Determine the probability that a technician is needed after a one-week period?
b. If you are the first one in the city to place an order, determine the probability that you have to wait more than two weeks from the time you place your order till a technician is dispatched?