# Critical Path and PERT

1) A PERT project has 45 activities, 19 of which are on the critical path. The estimated time for the critical path is 120 days. The sum of all activity variances is 64, while the sum of variances along the critical path is 36. The probability that the project can be completed between days 108 and 120 is

a) 0 -2.00

b) 0.0227

c) 0.1058

d) 0.4773

e) 0.9773

2) A project being analyzed by PERT has 38 activities, 16 of which are on the critical path. If the estimated time along the critical path is 90 days with a project variance of 25, the probability that the project will be completed in 88 days or less is

a) 0.0228

b) 0.3446

c) 0.6554

d) 0.9772

e) 18

3) Analysis of a PERT problem shows the estimated time for the critical path to be 108 days with a variance of 64. There is a .90 probability that the project will be completed before approximately day ________.

a) 98

b) 108

c) 109

d) 115

e) 118

https://brainmass.com/math/probability/critical-path-and-pert-436671

#### Solution Preview

Please see the attached file.

We assume that the probability of completion time is normally distributed.

Normal probability distribution has two parameters- average and standard deviation

The average time of completion is the sum of completion time for activities on the critical path.

The variance of the critical path is the sum of variances of the activities on the critical path.

Standard deviation is the square root of variance.

We read probability values using standard normal distribution table or use Excel worksheet function NORMSDIST.

Given the values of probability, we read z value using standard normal distribution table or use Excel worksheet function NORMSINV.

A PERT project has 45 activities, 19 of which are on the critical path. The ...