PERT is a scheduling method used to plan, schedule, and control projects. It employs a network of interrelated activities and coordinates costs and time criteria. The example project involves building a parade float over 26 weeks. PERT is used to identify the project's critical path of activities, calculate the probability of completing on time, and determine which path has the highest likelihood of completion within the deadline. The critical path is identified as A-C-F-I-K at 23 weeks, and there is a 98.30% probability of completing the entire project within the 26 week deadline.