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