A freighter has to be loaded with 2000 tons of hard coal. The coal arrives at the harbor by railway carriages each of which holds independently of each other a random load X with E(X) = 50 and Var(X)...

A freighter has to be loaded with 2000 tons of hard coal. The coal arrives at the harbor by railway carriages each of which holds independently of each other a random load X with E(X) = 50 and Var(X) = 64.

What is the smallest number n = n_min
of railway carriages which are necessary to make sure that with a probability of not less than 0.99 the freighter can be loaded with at least 2000 tons of coal?