A cement delivery company has a fleet of trucks that weigh 6,700 kg unloaded. The trucks are loaded with 800 bags of cement, each with a mean weight of 44 kg and a standard deviation of 5 kg. Assume that the bag weights are independent and identically distributed. Truck weights are limited to 42,000 kg to avoid damaging the road. a) What is the probability that the truck will have excess weight (i. e., above the 42,000 kg limit) less than 125 kg?
b) What is the probability that the truck will have excess weight between 125 kg and 200 kg?
c) What is the probability that the truck will have excess weight above 200 kg?