According to the PERT analysis, the probability distribution that should be used to represent the project's completion period is as follows:a.Poisson distributionb.Skewed distributionc.Normal distributiond.Beta distribution

To determine the probability distribution that should be used to represent the project's completion period according to the PERT analysis, we need to consider the characteristics of each distribution option.

a. Poisson distribution: The Poisson distribution is typically used to model the number of events occurring in a fixed interval of time or space. It may not be the most suitable choice for representing the project's completion period, as it focuses on discrete events rather than continuous time intervals.

b. Skewed distribution: The term "skewed distribution" is quite broad and can refer to various types of distributions, such as the skewed normal distribution or skewed exponential distribution. Without further information, it is difficult to determine if a skewed distribution would be appropriate for representing the project's completion period.

c. Normal distribution: The normal distribution, also known as the Gaussian distribution, is commonly used to represent continuous variables that are symmetrically distributed around a mean value. It assumes that the data follows a bell-shaped curve. While the normal distribution can be a reasonable choice for certain project variables, it may not accurately capture the uncertainty and variability associated with the project's completion period.

d. Beta distribution: The beta distribution is a versatile distribution that can be used to model a wide range of continuous variables. It is often employed in project management to represent uncertain variables with bounded values, such as the probability of success or failure. The beta distribution allows for flexibility in capturing different shapes and can be a suitable choice for representing the project's completion period, considering its inherent uncertainty and variability.

Based on the information provided, the most appropriate probability distribution to represent the project's completion period according to the PERT analysis would be the beta distribution (option d).