Q$3.$ Answer all parts

$[$Total $=30$ marks$]$

Figure $3\mathrm{.}1$ shows a PERT diagram for a project with durations in weeks.

Figure $3\mathrm{.}1-$ PERT Chart. O $-$ Optimistic, M $-$ Most Likely, P$-$ Pessimistic.

Create a table showing the task in the first column, with optimistic, most likely and

pessimistic times. Add two columns for expect time and variance.

a$)$ Calculate the expected time and the variance for each task and enter into the

table.

Expected time $=\frac{0+4m+p}{6}$

Variance of activity time $=[\frac{p-o}{6}{]}^2$

You may use MS Excel. Variance can be presented as $3$ significant

figures.

$(6$ marks$)$

b$)$ Draw the activity network diagram using the most likely time, and again using

the expected time. Identify the critical path both cases and comment on the

result.

Please round fractional values for Expected Time.