In one of my previous lives, a large online gaming operator called me up and asked me when a bug would be fixed in their software. I estimated that it would be fixed within three days. He then quizzed me, "Do you know what the problem is? Do you know how long it will take to fix, once you determined the problem? Do you have someone working on this right now?"
My answer to all his questions was, "no". He was furious. He was also a new contact at the gaming operator - and probably wanted to make his impact felt in everything he did. He screamed, "How can you claim it will be done in three days, then?"
I struggled to find words to articulate an answer. In hindsight, I should have just said, 'From experience, I know these problems don't ever take more than three days to fix'.
Estimating how long things take is often difficult, and people struggle with this every day. But experience often brings better judgement than most people imagine.