The error for the production of a machine is uniformly distributed over [0.5,0.3]unit. Assuming that there are200machines working at the same time, approximate the probability that the final total production differ from the exact total production by more than5unit?

From the above I have calculated that mean = -0.1, sd = 0.2309. For the final total production value, I know i have to use the central limit theorem, but i am using the sum version (ie. X~N(n, n)) where n=200, but am getting a Z value of above 7 and i don't think this is correct. I have seen other questions same as this but I don't understand how they have come to their answer. What am I doing wrong?