# Question

A manufacturer fills one-gallon cans (3,785 ml) on an assembly line in two independent steps. First, a high-volume spigot injects most of the paint rapidly. Next, a more precise but slower spigot tops off the can. The ll amount in each step is a normally distributed random variable. For step one, μ1 = 3,420 ml and σ2 = 10 ml, while for step two μ2 = 390 ml and σ2 = 2 ml. Find the mean and standard deviation of the total fill X1 + X2.

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