Question

A PERT project has 45 activities, 19 of which are on the critical path. The estimated time for the critical path is 120 days. The sum of all activity variances is 64, while the sum of variances along the critical path is 36. What is the probability that the project can be completed between days 108 and 120?A) 0.0227B) 0.1058C) minus−2.00D) 0.9773E) 0.4773

Answer 1

Answer:

0.4773

Step-by-step explanation:

The estimated time for the critical path, μ = 120 days

Sum of variances along the critical path = 36

Standard deviation of critical path δ, is therefore given as,

δ = $\sqrt{36}$

δ = $6$

1. Probability that the project can be completed between 108 and 120 days:

Z = days range / standard deviation

Z = (108 - 120) / 6

= - 2

Therefore, the probability that the project can be completed in less than 108 days = 0.0227 or 2.27%

Since the critical path is attained at half the time that it takes to complete the project,

Probability that the project duration is between 108 and 120 days = Probability at critical time - Probability when the duration is less than 108 days

P = 50% - 2.27%

= 47.73% or 0.4773

Answer 2

Answer:

P ( 108 < X < 120 ) = P ( -2 < Z < 0 ) = 0.4773

Option E

Step-by-step explanation:

Given:

- The estimated time for critical path u = 120 days

- The sum of variances along critical path Var = 36

Find:

What is the probability that the project can be completed between days 108 and 120?

Solution:

- The project always takes route of the critical path activities, hecne, we will ignore the activities that are not on critical path.

- We assume that the probability of completion time is normally distributed.

Normal probability distribution has two parameters- average and standard deviation.

- We will assign a random variable X as the number of days to complete activities on critical path. So,

                            X~ N ( 120 , sqrt(36) )

- We need to find the probability, compute the corresponding Z-scores:

      P ( 108 < X < 120 ) = P ( (108 - 120)/ 6 < Z < 0 )

- Use the Z-Tables to look up the required probability:

     P ( -2 < Z < 0 ) = 0.4773

Hence,

      P ( 108 < X < 120 ) = P ( -2 < Z < 0 ) = 0.4773