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 fill amount in each step is a normally distributed random variable. For step one, μ1 5 3,420 ml and σ2 5 10 ml, while for step two μ2 5 390 ml and σ2 5 2 ml. Find the mean and standard deviation of the total fill X1 1 X2.

A manufacturing project has five independent phases whose completion must be sequential. The time to complete each phase is a random variable. The mean and standard deviation of the time for each phase are shown below. (a) Find the expected completion time. (b) Make a 2-sigma interval around the mean completion time (μ 6 2σ).

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