Final answer:
To calculate the expected time and standard deviation for each activity, use the three-point estimate formula. The probability of completing the project in 200 days is close to 0.
Step-by-step explanation:
To calculate the expected time and standard deviation for each activity in the project, we can use the three-point estimate formula. The expected time (TE) can be calculated using the formula:
TE = (a + 4m + b) / 6
The standard deviation (SD) can be calculated using the formula:
SD = (b - a) / 6
Using these formulas, we can calculate the expected time and standard deviation for each activity:
Activity A: TE = (15 + 4(36) + 52) / 6 = 36 days, SD = (52 - 15) / 6 = 6.17 days
Activity B: TE = (45 + 4(62) + 82) / 6 = 68.5 days, SD = (82 - 45) / 6 = 6.17 days
Activity C: TE = (34 + 4(36) + 38) / 6 = 36 days, SD = (38 - 34) / 6 = 0.67 days
Activity D: TE = (16 + 4(26) + 38) / 6 = 28 days, SD = (38 - 16) / 6 = 3.67 days
Activity E: TE = (34 + 4(36) + 40) / 6 = 36 days, SD = (40 - 34) / 6 = 1 days
Activity F: TE = (32 + 4(38) + 44) / 6 = 38 days, SD = (44 - 32) / 6 = 2 days
To calculate the probability that the project will be completed in 200 days, we need to calculate the sum of expected times for all activities and the sum of the variances:
Sum of expected times = 36 + 68.5 + 36 + 28 + 36 + 38 = 242.5 days
Sum of variances = 6.17^2 + 6.17^2 + 0.67^2 + 3.67^2 + 1^2 + 2^2 = 75.58
Standard deviation of the project = sqrt(sum of variances) = sqrt(75.58) = 8.7 days
Z score = (200 - 242.5) / 8.7 = -4.86
Using a z-table or calculator software, the probability of completing the project in 200 days or less is close to 0.