Worth noting that Metaculus has the ability to record continuous distribution predictions, including both normal predictions and much more complicated distributions. E.g. https://www.metaculus.com/questions/5301/a-city-exodus/
If you want to record your predictions for your own questions on Metaculus you can also create private questions here. https://www.metaculus.com/questions/create/
Worth noting that Metaculus has the ability to record continuous distribution predictions, including both normal predictions and much more complicated distributions. E.g. https://www.metaculus.com/questions/5301/a-city-exodus/
If you want to record your predictions for your own questions on Metaculus you can also create private questions here. https://www.metaculus.com/questions/create/