A project manager and a stakeholder have different opinions on the budget estimates for a...

According to the PMBOK Guide, 6th edition, section 6.4.2.6, the Monte Carlo method is a simulation technique that uses probability distributions and random sampling to compute possible outcomes of cost or schedule estimates.3

The Monte Carlo method can produce different results each time it is run, depending on the input data and the random numbers generated.4

Therefore, the project manager and the stakeholder may have used different input data, assumptions, or scenarios when applying the Monte Carlo method, resulting in different estimations for the budget.4

The project manager and the stakeholder should compare and validate their estimations, and agree on a common baseline for the budget.

The references for this answer are:

1: PMP Exam Questions | 100% Free PMP Example Questions 2: PMP Practice Exam 1 | Free PMP Exam Questions 3: PMBOK Guide, 6th edition, Project Management Institute, 2017, pp. 200-201. 4: [Monte Carlo Simulation: What Is It and How Does It Work? - Palisade] : [Project Cost Management: The Ultimate Guide - ProjectManager.com]