Question

The expected times and variances for the project activities are given below. Complete the table showing which activities are critical.

ID	Description	Predecessor	Te	Variance	Critical?
1	Pilot Production	None	6	3	?
2	Select Channels of Distribution	None	20	4	?
3	Develope Mktg. Program	None	18	2	?
4	Test Market	1	4	2	?
5	Patent	1	17	5	?
6	Full production	4	9	10	?
7	Ad Promotion	3	16	2	?
8	Release	2,5,6,7	2	1	?

What is the probability of completing the project in 27 periods? Hint: Use the =NORM.S.DIST(z, TRUE) function in Excel to compute the probability. (Do not round intermediate calculations. Round the final answer to 3 decimal places, i.e., 0.750.)

1). What is the probability of completing the project in 27 time periods?_____

***PLEASE SHOW ALL WORK! I AM TRYING TO LEARN :)***

Answer 1

Solution:
To fin Critical path and duration of project, we will create Network diagram, forward and backward pass

From the forward and backward pass, we found that critical path is 3-7-8 with critical time (18+16+2) = 36
Critical activities are those activities which have zero slack. So Critical activities are 3, 7 and 8

ID	Te	Variance	Critical?
1	6	3	No
2	20	4	No
3	18	2	Yes
4	4	2	No
5	17	5	No
6	9	10	No
7	16	2	Yes
8	2	1	Yes

We need to calculate probability that the project will complete in 27 periods
Critical time = 36 periods
Variance = (2+2+1) = 5 periods
Standard deviation = sqrt(5) = 2.24
Z-score = (X-mean)/Standard deviation = (27-36)/2.24 = -4.02
From normal distribution table we found p-value
P(X<=27 periods) = 0.000029
So there is 0.003% probability of completing the project in 27 periods.