e) The activity variance along the critical path is ________ weeks. (Round your

Question

e) The activity variance along the critical path is ________ weeks. (Round your response to two decimal places).

f) The probability that Hopkins Hospitality will finish the project in 36 weeks or less is ________. (Enter as a probability and round your response to three decimal places).

Homework: Chapter 3 Project Management Hw Score: 28.4%, 5.1 1 of 18 pts Score: 0.67 of 2 pts %) Problem 3.17b Ross Hopkins, president of Hopkins Hospitality, has developed the tasks, durations, and predecessor relationships in the following table for building new motels 8 of 10 (7 complete) Question Help Immediate Predecessor(s) Time (weeks) Immediate Time (weeks) b Activity a m b Predecessor(s) Activity a C, E 1 8 24 C 9 14 16 5 6 10 D, G, H I, J 12 8 20 C, E a) The expected (estimated) time for activity C is 13.5 weeks. (Round your response to fwo decimal places,) b) The variance for activity C is 1.3611 weeks. (Round your response to two decimal places) c) Based on the calculation of the estimated times, the critical path is A-C-F-H-J-K d) The estimated time for the critical path s weeks. Round your response to two de al places) Enter your answer in the answer box and then click Check Answer. Check Answer Clear All parts remaining

Explanation / Answer

We take that critical path as given in answer #c = A-C-F-H-J-K

The estimated time of the critical path

= Sum of expected duration of corresponding activities i.e. A,C,F,H,J,K

= 8 + 13.5 + 9.5 + 2 + 7.67 + 1.5

= 42.17 weeks

THE ESTIMATED TIME FOR THE CRITICAL PATH IS 42.17 WEEKS

Activity variance along the critical path

= Sum of variances of corresponding activities i.e. A,C,F,H, J , K

= 1.78 + 1.36 + 6.25 + 0 + 1 + 0.25

= 10.64 weeks

ACTIVITY VARIANCE ALONG THE CRITICAL PATH = 10.64 WEEKS

Standard deviation of duration of critical path = Square root ( Variance ) = Square root ( 10.64 ) = 3.26 weeks

Let Z value for corresponding probability that the project will complete in maximum 36 weeks = Z1

Accordingly,

Expected duration of critical path + Z1 x Standard deviation of critical path = 36

Or, 42.17 + 3.26.Z1 = 36

Or, 3.26.Z1 = 36 – 42.17 = - 6.17

Or, Z1 = - 6.17 / 3.26 = - 1.89

Corresponding probability for Z = - 1.89 s derived from standard normal table = 0.02938 ( 0.029 rounded to 3 decimal places )

PROBABILITY THAT HOPKINS HOSPITALITY WILL FINISH THE PROJECT IN 36 WEEKS OR LESS IS 0.029

THE ESTIMATED TIME FOR THE CRITICAL PATH IS 42.17 WEEKS

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