## Ytg

The last two activities, I and ), are drawn in the same manner. Activity 1 requires that both g and h be completed, so g and h are directed to a single node (node 5). Similarly, activity j requires the completion of both d and e, which are directed to node 6. Since no activities require that f, i, or) precede them, these activities are directed to the project completion node, 7. The complete project network is shown in Figure 8-13.

The next step is to calculate expected activity completion times from the data in Table 8-1. These expected completion times are found by using the three time estimates (optimistic, pessimistic, and most likely) in the table.

Once again, a short digression is helpful. Precisely what is meant by "optimistic," "pessimistic," and "most likely"? Assume that all possible times for some specific activity might be represented by a statistical distribution (e.g., the asymmetrical distribution in Figure 8-14). The "most likely" time, m, for the activity is the mode of this distribution. In theory, the "optimistic" and "pessimistic" times are selected in the following way. The PM, or whoever is attempting to estimate a and b, is asked to select a such that the actual time required by the activity will be a or greater about 99 percent of the time. Similarly, b is estimated such that about 99 percent of the time the activity will have a duration of b or less. (We know of no project managers or workers who are comfortable making estimates at this level of precision, but we will delay dealing with this problem for the moment.) 