Drums labeled 30 L are filled with a solution from a large vat. The amount of solution put into each drum is random with mean 30.01 L and standard deviation 0.1 L.

a. What is the probability that the total amount of solution contained in 50 drums is more than 1500 L?

b. If the total amount of solution in the vat is 2401 L, what is the probability that 80 drums can be filled without running out?

c. How much solution should the vat contain so that the probability is 0.9 that 80 drums can be filled without running out?