The volumes of chemical reagent in Grade A containers follow a normal distribution with mean 250 ml and standard deviation 4.5 ml. The volumes in Grade B containers follow a normal distribution with mean 242 ml and standard deviation 3.8 ml.
A single container of each grade is selected at random.
Calculate the probability that the Grade A container contains a smaller volume of reagent than the Grade B container.
A laboratory batch is formed by taking 4 Grade A containers and 6 Grade B containers chosen at random.
Determine the probability that the total volume of reagent in the batch is more than 2460 ml.
