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
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 = [tex]\sqrt{36}[/tex]
δ = [tex]6[/tex]
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
