e The activity variance along the critical path is weeks Ro

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

Solution

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