A small project is composed of seven activities, whose time estimates are listed in the table below: A small project is composed of seven activities, whose time estimates are

listed in the table below:

i$)$ Draw the network diagram of activities in the project.

ii$)$ Find the expected duration and variance for each activity. What is the

expected project length?

iii$)$ Calculate the variance and standard deviation of the project length.

What is the probability that the project will be completed atleast $4$

weeks earlier than expected time.

Activity $($i $$ j$)$ Estimated Duration $($Weeks$)$

Optimistic Most Likely Pessimistic

$12117$

$13147$

$14228$

$25111$

$352514$

$46258$

$563615$

i$)$ Draw the network diagram of activities in the project.

ii$)$ Find the expected duration and variance for each activity. What is the expected project length?

iii$)$ Calculate the variance and standard deviation of the project length. What is the probability that the project will be completed atleast $4$ weeks earlier than expected time.

Z $0\mathrm{.}671\mathrm{.}001\mathrm{.}332\mathrm{.}00$

Prob. $0\mathrm{.}25140\mathrm{.}15870\mathrm{.}09180\mathrm{.}0228$