Problem 17-7 Three recent college graduates have formed a partnership and have o
ID: 2746595 • Letter: P
Question
Problem 17-7
Three recent college graduates have formed a partnership and have opened an advertising firm. Their first project consists of activities listed in the following table. Use Table B.
TIME IN DAYS
What is the probability that the project can be completed in 24 days or less? In 21 days or less? (Round your te and z values to 2 decimal places and "Standard deviation" to 3 decimal places. Round your final answers to 4 decimal places.)
Suppose it is now the end of the seventh day and that activities A and B have been completed while activity D is 50 percent completed. Time estimates for the completion of activity D are 5, 6, and 7. Activities C and H are ready to begin. Determine the probability of finishing the project by day 24 and the probability of finishing by day 21. (Round your intermediate calculations to 3 decimal places and final answers to 4 decimal places.)
Three recent college graduates have formed a partnership and have opened an advertising firm. Their first project consists of activities listed in the following table. Use Table B.
Explanation / Answer
Activity Immediate Predecessor Optimistic Most Likely Pessimistic Expected Time Variance A — 5 6 7 6.00 0.11 B — 8 8 11 8.50 0.25 C A 6 8 11 8.17 0.69 D — 9 12 15 12.00 1.00 E C 5 6 9 6.33 0.44 F D 5 6 7 6.00 0.11 G F 2 3 7 3.50 0.69 H B 4 4 5 4.17 0.03 I H 5 7 8 6.83 0.25 End E, G, I 61.50 3.58 *Expected = (Optimistic + 4 * Probable + Pessimistic) / 6 Variance = (Pessimistic - Optimistic / 6)^2 Standard Deviation = Variance Paths Duration Days A-C-E 6+8.17+6.33 20.50 B-H-I 8.5+4.17+6.83 19.50 D-F-G 12+6+3.50 21.50 Critical path Critical path = D-F-G Expected Time = 21.50 days Variance = 1.8056 days Standard Deviation = 1.3437 days a. Probability that project will be completed in 24 days or less x 24 Z = X - Mean /Sd = 24 - 21.50 / 1.3437 Z = 1.861 From Z tables, we get, Required Probability = 0.9686 OR 96.86% b. Probability of completing project in 21 days or less x 21 Z = X - Mean /Sd = 21 - 21.50 / 1.3437 Z = -0.372 From Z tables, we get, Required Probability = 0.3549 OR 35.49% Activity C and H are non critical acitivities. So those do not impact project complete date even if completed earlier However, Activity D is critical activity, hence new Completion time and Variance are calculated as below Mean Variance D 6.00 0.11 F 6.00 0.11 G 3.50 0.69 15.50 0.92 SD = 0.9574 c. Probability that project will be completed in 24 days x 24 - 7 = 17 Z = X - Mean /Sd = 17 - 15.50 / 0.9574 Z = 1.5667 From Z tables, we get, Required Probability = 0.9414 OR 94.14% d. Probability that project will be completed in 21 days x 21 - 7 = 14 Z = X - Mean /Sd = 14 - 15.50 / 0.9574 Z = -1.5667 From Z tables, we get, Required Probability = 0.0586 OR 5.86%