1. A factory has a delicate process that is affected by weather. If it rains, decrease the humidity inside the factory to continue operations. Since inside the factory the rain is no heard it is known that the probability of the work being damaged given that nobody noticed in time is 33%. If you have 85 rainfalls in a year calculate the expected number of damaged works and variance.
2. On average, every six minutes a car passes by a sector in which it plans to build a tunnel. The passage of many vehicles indicate risk of congestion in the new construction. The engineers in charge of the project need to determine whether the probability that in one hour more than 5 vehicles that circulate by the sector is less than 0.04.