A small elevator has a maximum capacity $C$, which is normally distributed, with mean $400$ kg., and standard deviation $4$ kg. The weight of the boxes being loaded into the elevator is a random variable with mean $30$ kg., and standard deviation $0.3$ kg.
Assume that the weights of the boxes and maximum capacity are independent random variables. How many boxes may be loaded into the elevator before the probability of disaster exceeds $20\%$?
I've found so far that:
With $X$ being the weight of the boxes and $C$ being the weight of the elevator.
But I can't seem to figure out where to go from here.