Question

HW Score: 62.5%,5 of The estimated times and immediate predecessors for the activities in a projects Howard Urinalarning company are given in the following assume that the activity times are independent Question Help Activity . Immediate Predecessor) А 8 Time (weeksi . Predecessors Activity b 8 10 С 7 19 13 4 10 18 D 6 10 14 This exercise contains only parts , bedande a) Based on the activity time estimate the expected times and variance for each of the cities we found your one we decine Expected Activity Time Variance A 0.25 10:35 5:44 с 10.00 D 10.00 178 00 b) The expected completion time of the critical path 20 33 weeks round your response to two decalcol The expected completion time of the path other than the critical path 1983 weeks Yound your response to two decimal places) c) The variance of the critical path = 7.22 weeks fround your response to two decimal places! The variance of the path other than the critical path 125 weeks fround your response to two decimal places). d) If the time to complete the activities on the critical path is normally distributed, then the probability that the critical path will be finished in 23 weeks or less For as a probably and round your response to two decimal placea).

Answer 1

We solve the given problem using POM-QM as shown below:

We enter the required data as shown below:

Activity Optimistic time Predecessor Predecessor 2 1 А B с D 8 4 7 Most Likely Pessimistic time time 10 11 10 18 10 13 10 14 А B 6

On solving, we get

Activity Early Finish Late Start time Late Finish Slack Standard Deviation Variance Project A B с D Activity Early Start 20.33 9.83 0 10.33 0 10 9.83 10 10.33 2.69 .5 2.33 7.22 25 5.44 9.83 10.33 19.83 20.33 .5 0 10.33 10.33 10.33 10.33 20.33 20.33 .5 0 .5 0 1 1 1.33 1.78

Hence, as seen from above, the answers for part a, b, c, are correct

d) Required duration = R = 23 weeks

Expected duration = E = 20.33 weeks

Std. Deviation = $\sigma$ = 2.69

We get the Z value as:

Z =
R Ε
= $\frac{23-20.33}{2.69}$ = 0.993

For Z = 0.99, the probability from Z table = 0.8389 = 83.89%

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