$5.$ In a CPM network, the critical path has five activities. Their durations are tabulated

next.

Compute the following:

a$.$ The probability that the project will finish by the end of day $32$

b$.$ The probability that the project will finish by the end of day $34$

c$.$ The probability that the project will finish before day $30$

d$.$ The probability that the project will finish on day $32$

e$.$ The probability that the project will finish no later than day$35$

A$.$

Activity Optimistic time Most likely time Pessimistic time Expected completion time of activity Std$.$ Deviation Variance

A $2595\mathrm{.}171\mathrm{.}16666666666666671\mathrm{.}3611111111111114$

B $3484\mathrm{.}50\mathrm{.}83333333333333340\mathrm{.}6944444444444445$

C $4696\mathrm{.}170\mathrm{.}83333333333333340\mathrm{.}6944444444444445$

D $5102010\mathrm{.}832\mathrm{.}56\mathrm{.}25$

E $3595\mathrm{.}3311$

Sum $326\mathrm{.}33333333333333410$