The standard deviation of the critical path is a measure of the variability or uncertainty in the completion time of the project. It helps in understanding the risks associated with the project schedule and aids in making informed decisions regarding project management. In this case, the correct answer is option 'C' which is 0.88.

Here, we will discuss the concept of critical path, its standard deviation, and how it is calculated.

Critical Path:
The critical path is the longest sequence of dependent activities that determines the total duration of a project. It represents the shortest possible time required to complete the project. Any delay in the activities on the critical path will directly impact the overall project completion time.

Standard Deviation:
The standard deviation is a statistical measure that quantifies the amount of variation or dispersion in a set of values. It provides insight into the spread of data points around the mean value. In the context of project management, the standard deviation of the critical path helps in estimating the uncertainty or variability in the project completion time.

Calculating the Standard Deviation of the Critical Path:
To calculate the standard deviation of the critical path, we need to determine the duration and standard deviation of each activity on the critical path. The standard deviation of an activity can be obtained using the PERT (Program Evaluation and Review Technique) analysis, which considers optimistic, pessimistic, and most likely time estimates.

The standard deviation of the critical path is the square root of the sum of the variances of individual activities on the critical path. The variance of an activity is calculated as the square of the standard deviation.

Mathematically, the standard deviation of the critical path can be expressed as:
Standard Deviation = √(∑(Variance of activities on the critical path))

In this case, the correct answer is option 'C' which is 0.88. This implies that the sum of the variances of activities on the critical path is 0.88 squared units.

To determine the specific values of variances and calculate the standard deviation, more information about the project and the critical path is required. The given options represent the different values of the standard deviation, and option 'C' is the correct one based on the given information.