Question

Discuss how the Central Limit Theorem simplifies calculations relating to PERT by converting skewed distributions of individual activities into normally distributed paths of activities. How do we then compute the probability of completing a project within a specified duration?

Answer 1

CLT is a statistical theory stating that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population. Furthermore, all the samples will follow an approximate normal distribution pattern, with all variances being approximately equal to the variance of the population, divided by each sample's size.

The main idea of the central limit theorem (CLT) is that the average of a sample of observations drawn from a population with any distribution shape is approximately distributed as a normal distribution if certain conditions are met. More precisely, the central limit theorem states that given a distribution with a mean μ and variance σ², the sampling distribution of the mean approaches a normal distribution with a mean (μ) and a variance σ²/n as n, the sample size, increases. The amazing and counter-intuitive thing about the central limit theorem is that no matter what the shape of the original distribution is, the sampling distribution of the mean approaches a normal distribution.

When it comes to PERT, The project duration follows a normal distribution with the following parameters:

• Average = E(D) = expected project duration (based on critical path)
• Variance = E(V) = expected variance (of the critical path)