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
