3 of 8 Problem2 Qatar University has a project which was planned using PERT wth

Question

3 of 8 Problem2 Qatar University has a project which was planned using PERT wth three time estimates. The expected completion time of the project was determined to be 40 weeks. The varance of the critical path is s9 5 Marks) (a) What is the probability that the project will be finished in 40 weeks or less? (b) What is the probability that the project will take longer than 46 weeks? (c) I the contracting company has agreed in the contract to pay an amount of 2 ilion Qatani Ryal f the project is completed in a period, which is one month longer than the expected completion time, what is the probability that the contracting company is going to pay the penalty? a The projedt manager wishes to set the due date for the compleion of the projedt so that there is a9%dance of finishing on schedule. Thus, there would only be a 10% chance the project would take longer than this due date. What should this due date be? (5 Marks) Problem 3 A construction company in Doha is implementing the plan to construct a lab for Qatar University. The project's details are illustrated in the following Table Nomal Crash Activity Predecessors Tme Tme Normal Crash Crash weeks (weeks cost per cost cos 7,000 | 8.000

Explanation / Answer

Please find answer to Question 2 :

Answer to # a:

Expected completion time of the project = m = 40 weeks

Variance of the project = 9 weeks

Hence, Standard deviation of the project duration = Sd = Square root ( 9) = 3 weeks

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

Thus,

M + Z1x Sd = 40

Or, 40 + 3Z1 = 40

Or, Z = 0

Corresponding probability for Z = 0 is 0.5

Hence, probability that project will finish in 40 weeks or less = 0.5

Answer to #b:

Let Z value for probability that project will take max 46 weeks = Z2

Thus,

40 + 3.Z2 = 46

Or, Z2 = 2

Corresponding probability for Z2 = 2 as derived from standard normal distribution table = 0.97725

Therefore, Probability that project will take longer than 46 weeks

= 1 – Probability that project finish in 40 weeks or less

= 1 – 0.97725

= 0.02275

PROBABILITY THAT PROJECT WILL TAKE LONGER THAN 46 WEEKS = 0.02275

Answer to # c:

Target project completion time = Expected completion time + 1 week = 40 + 1 = 41 weeks

Let, corresponding Z value for probability of completing the project in 41 weeks = Z3

Therefore,

M + Z3 x Sd = 41

Or, 40 + 3, Z3 = 41

Or, Z3 = 0.33

Corresponding value of probability for Z = 0.33 as derived from standard normal distribution table = 0.62930

Thus,

PROBABILITY THAT THE CONTRACTING COMPANY IS GOING TO PAY THE PENALTY = 0.62930

Answer to #d:

90% chance of finishing on schedule means probability of completing the project within corresponding time is 0.90

Corresponding Z value for probability 0.90 = NORMSINV ( 0.90) = 1.2815

Thus due date of project completion time

= Expected duration x Z valeue x Standard deviation of duration of project

= 40 + 1.2815 x 3

= 40 + 3.844

= 43.844 weeks

DUE DATE IS 43.844 WEEKS

PROBABILITY THAT PROJECT WILL TAKE LONGER THAN 46 WEEKS = 0.02275

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