Question 1 (35 points) Consider the project network given in the following figure where the expected duration in days and the variance (in parenthesis) are indicated. 6(2) 5(2) 7(3) 4 5 3(1) Start 8 5(2) 2 3 8(2) 4(1) 6(1) a) (16 points) Determine the critical path. b) (9 points) What is the effect of each of the followings on the duration of the entire project? (Consider each independently, and assume the durations of the rest of the activities do not change) a. Activity 5 is delayed by 3 days b. Activity 6 is delayed by 3 days c. Activity 7 is delayed by 3 days c) (10 points) Assuming that activities are independent and that the central limit theorem applies, what is the probability that project completes on the 27th day or later