Question

2. Given the project information below, what is the probability of completing the National Holiday Toy project in 93 time units?

Note 1: The Critical Path activities are: 1, 2, 4, 5, 6, 7. Note 2: Using the examples in Appendix 7.1 as a guide, calculate the weighted average activity time of each task (t_e). Determine the project duration. Calculate the variance. Use the Z-score formula, in Appendix 7.1 to calculate the Z-score. Note that non-critical path activities are not included in Z-score calculations. Also be aware that a critical path activity may not need to be included, if it occurs parallel with another critical path activity and has the same t_e. Then use the statistical table A7.2 (or look for a Z-score table on the Internet, because the one is the text is abbreviated) and find the probability of completing the project in 93 time units.  

ID	Description	Predecessor	(a)	(m)	(b)	te	Variance
1	Design package	none	6	12	24
2	Design product	1	16	19	28
3	Build package	1	4	7	10
4	Secure patent	2	21	30	39
5	Build product	2	17	29	47
6	Paint	3, 4, 5	4	7	10
7	Test market	6	13	16	19

Answer 1

Here we have 2 critical paths which are parallel to each other 1-2-4-6-7 and 1-2-5-6-7

Project duration = duration of the longest path (Critical path) = 86 time units

We know, z = (x-expected project completion time)/project standard deviation

When x = 93,

Z = (93-86)/sqrt(24) = 1.428869017

So, probability of completing the project within 93 time units = norm.s.dist(1.428869017,TRUE) = 0.923479058

Formula