Question

Three recent college graduates have formed a partnership and have opened an advertising firm. Their first project consists of activities listed in the following table. Use Table B.

		TIME IN DAYS
Activity	Immediate Predecessor	Optimistic		Most Likely			Pessimistic
A	—	5		6			7
B	—	8		8			11
C	A	6		8			11
D	—	9		12			15
E	C	5		6			9
F	D	5		6			7
G	F	2		3			7
H	B	4		4			5
I	H	5		7			8
End	E, G, I

b.What is the probability that the project can be completed in 24 days or less? In 21 days or less? (Round your t_e and z values to 2 decimal places and "Standard deviation" to 3 decimal places. Round your final answers to 4 decimal places.)

Days	Probability
24 days or less
21 days or less

c. Suppose it is now the end of the seventh day and that activities A and B have been completed while activity D is 50 percent completed. Time estimates for the completion of activity D are 5, 6, and 7. Activities C and H are ready to begin. Determine the probability of finishing the project by day 24 and the probability of finishing by day 21. (Round your intermediate calculations to 3 decimal places and final answers to 4 decimal places.)

	Probability
Day 24
Day 21

rev: 04_24_2019_QC_CS-166426

Answer 1

Network Diagram:

Expected Time = (a + 4m + b) / 6

We also neeed to calculate the variance of activities on the critical path:

Variance = 1.81

Ans b) Probability of that the project can be completed in 24 days or less?

Here X =24,

Step 1: Find the value of Z

Step 2: Find the value of probability for the calculated Z from the Normal Distribution Z table.

From Z-table,

P = 0.96856 = 96.86%

For X = 21

From Z-table

P = 0.35569 = 35.57 %

Ans C)

At the end of 7th Day, Activity A and B are completed. Activity D is completed 50% and Time estimates are 5,6 and 7.

So Expected time to complete remaining part of Activity D = (5 + 4*6 + 7)/6 = 6

So Activity D will be completed at the end of 13th Day instead of expected time 12 earlier.

Critical path will remain same.

Now, Expected time of Project completion = 22.50 Days

Probability of that the project can be completed in 24 days or less

Here X =24,

Step 1: Find the value of Z

Step 2: Find the value of probability for the calculated Z from the Normal Distribution Z table.

From Z-table,

P = 0.86650 = 86.65 %

For X = 21

From Z-table

P = 0.13350 = 13.35 %