The time and duration estimates produced by conventional planning tools are usually the Expected Value (EV), also known as the mean or the average. In most cases the EV is very close to the median – the 50% probability region.
The thing is, 50% is also the region of greatest uncertainty, subjective and objective. Heads you're under budget, tails you're over budget.
That doesn't seem like a wise choice. Especially since it's between a little under budget and a lot over budget. There's this thing called Jensen's Inequality. One of the ways it gets you is that there's a limit to how little a project will cost but there's no limit to how much it will cost.
As Sam Savage has pointed out many times many ways: On average, the average is wrong. So when you're tempted to perpetuate the Flaw of Averages, use a distribution instead.