a. Draw the project network. (5%) b. What is the expected completion time of the project? (10%) (i.e., must list all the possible paths and find the longest one as the expected completion path) c. If one path has the longest expected completion time, why is it not necessarily the critical path? (5%) d. What are the variances for each activity?(10%) e. Assuming that the path completion times are independent, what is the probability of completing the project in 40 weeks? (10%) f. Given the same assumption as in part (e), what is the probability of completing the project in 32 weeks? (10%) 3. What are the common characteristics of projects (as opposite from programs)? How do these characteristics increase the complexity and difficulty of achieving success in project management? Please discuss these differences in characteristics. (5%) 4. How does a poka-yoke improve quality. Please describe and explain the three types of mistake-prevention (3%)? Give one example that applies this mistake-prevention principle in health care. (2%)