I do not understand how to do the probability at the bottome of this problem. Pl

Question

I do not understand how to do the probability at the bottome of this problem. Please help!

Ross Hopkins, president of Hopkins Hospitality, has developed the tasks, durations, and predecessor relationships in the following table for building new motels Time (weeks) Immediate Time (weeks)Immediate b Predecessor(s) b PredecessorsActivity a 12 24 16 Actvty a m C, E 8 12 12 D, G, H 21 C, E a) The expected (estimated) time for activity C is 12.17 weeks. (Round your response to two decimal places.,) b) The variance for activity C is 1.36 weeks. (Round your response to two decimal places.) c) Based on the calculation of the estimated times, the critical path is A B E-F-H-J- K d) The estimated time for the critical path is 45.1 weeks. (Round your response to two decimal places.) e) The activity variance along the critical path is 22.75 weeks. (Round your response to two decimal places.) f The probability that Hopkins Hospitality will finish the project in 40 weeks or less is (Enter as a probability and round your response to three decimal places,)

Explanation / Answer

The estimated time for critical path = 45.1 weeks

The activity variance along the critical path = 22.75 weeks

Therefore. Standard deviation of activities along the critical path = Square root ( 22.75 ) = 4.77 days

Let , Z value corresponding to the probability that the project will be finished in 40 weeks or less = Z1

Accordingly,

Expected time of critical path + Z1 x Standard deviation of critical path = 40

Or, 45.1 + 4.77xZ1 = 40

Or, 4.77.Z1 = 40 - 45.1 = - 5.1

Or, Z1 = - 5.1/4.77 = - 1.07

Corresponding value of probability for Z1 = - 1.07 as derived from standard normal distribution table = 0.14231 ( 0.142 rounded to 3 decimal places )

PROBABILITY THAT HOPKINS HOSPITAL WILL FINISH THE PROJECT IN 40 WEEKS OR LESS IS 0.142

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