A factory produces bags of cement. The weight of a bag of cement is modeled by a normal distribution with mean 50.5 kg50.5\text{ kg}50.5 kg and standard deviation 0.45 kg0.45\text{ kg}0.45 kg.
Find the probability that the weights of two randomly selected bags of cement differ by more than 0.80 kg0.80\text{ kg}0.80 kg.
Bags of cement are randomly selected and loaded onto transport crates. The weight of an empty crate is modeled by a normal distribution with mean 45.0 kg45.0\text{ kg}45.0 kg and standard deviation 1.20 kg1.20\text{ kg}1.20 kg.
Each fully loaded crate contains 20 bags of cement.
Find the probability that the total weight of a randomly selected fully loaded crate is less than 1050 kg1050\text{ kg}1050 kg.
