Question

Time estimates Expected Variance

Activity Optimistic Most Likely Pessimistic Time (ET) (s)
a m b
A 41 50 59
B 54 60 66
C 58 70 80
D 32 41 44

A → C
↗ ↘
Start End
↘ ↗
B → D

What is the estimated expected (mean) time for project completion?

a. 221 days
b. 70 days
c. 120 days
d. 41 days
e. 100 days

Answer 1

Using the formula ET = (a + 4m + b) / 6, the expected times for activities A, B, C, and D are computed and summed based on the pathway from start to end. For activities A and C, which represent the series required for project completion, the total expected time is 119.67 days. The closest answer is 120 days, corresponding to option c.

Step-by-step explanation:

The expected time for each activity can be calculated using the formula:

ET = (a + 4m + b) / 6

• For activity A: ET = (41 + 4(50) + 59) / 6 = (41 + 200 + 59) / 6 = 300 / 6 = 50 days
• For activity B: ET = (54 + 4(60) + 66) / 6 = (54 + 240 + 66) / 6 = 360 / 6 = 60 days
• For activity C: ET = (58 + 4(70) + 80) / 6 = (58 + 280 + 80) / 6 = 418 / 6 = 69.67 days
• For activity D: ET = (32 + 4(41) + 44) / 6 = (32 + 164 + 44) / 6 = 240 / 6 = 40 days

The project is a series of activities A to C, and B to D. To find the estimated project completion time, add the expected times for each series of activities:

Total ET = A + C = 50 + 69.67 = 119.67 days

The closest answer to 119.67 days is 120 days, which is option c.