You can plug your numbers into a spreadsheet and let the computer calculate Te. For many people, it is to give him or her your most optimistic time. Its as if your mind wipes out all of your experiences and only focuses on that one time everything came together. You can't do it in that time very often, and once you say it, the boss expects it to happen. Using the weighted average will at least make you think about the possibilities.
Lets look at a hypothetical task.
In your project, you have to cut power to a hospital emergency room facility to connect up new equipment. The hospital has back-up generators but they want to know how long it will take to be sure they have enough reserve power. We might need a little more certainty that 50 percent in this situation. To add to our probability of getting done on time, we can increase our time by adding a standard deviation. Te is a weighted average using your most optimistic, most pessimistic and most likely times.