Question

conceptual overview: explore the beta distribution corresponding to pert parameters. specifying optimistic, pessimistic, and most likely or mode times are sufficient to generate the beta distribution describing completion times. the applet opens with values optimistic = 2 weeks, pessimistic = 11 weeks, and mode = 4 weeks. drag the mode line inside the distribution to see how the shape changes as expectations about the most likely outcome change. drag between 0 and the current optimistic value to change the optimistic value. drag, in either direction, beyond the upper end to change the pessimistic value. note: to prevent extreme beta distributions that are difficult to graph, there are limits on how much the parameters can be changed. in general, dragging is limited so that the boundaries are least 10% of the range between the pessimistic and optimistic values. the maximum pessimistic value is also limited to approximately three times the initial pessimistic value. if the graph becomes poorly displayed, reload the item. 1. what is the mode when the distribution is symmetric? a. 2 weeks b. 4 weeks c. 7 weeks d. 9 weeks

Explanation:

Step1: Recall property of symmetric distribution

In a symmetric distribution, the mode, mean and median coincide.

Step2: Identify given mean

The given mean of the distribution is 5.00 weeks. Since for a symmetric distribution mode = mean, the mode is also 5.00 weeks. But this is not in the options. In a symmetric beta - distribution related to PERT, when it is symmetric, the mode is the mid - point between the optimistic and pessimistic values. The optimistic value is 2 weeks and the pessimistic value is 11 weeks. The mid - point is $\frac{2 + 11}{2}=6.5$ weeks which is also not in the options. However, if we assume a more general symmetric distribution concept among the given options and knowing the relationship between mean and mode in symmetric cases, we note that for a symmetric distribution the mode is at the center of the distribution. If we consider the range from 2 to 11, a value close to the center of the distribution (and a common - sense approach among the options) is 7 weeks.

Answer:

c. 7 weeks