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, Î¼1 5 3,420 ml and Ïƒ2 5 10 ml, while for step two Î¼2 5 390 ml and Ïƒ2 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 (Î¼ 6 2Ïƒ).