How do I convert a percentage from a 1%-100% scale to a different scale?

Question

So if I have 9%, and this 9% fits in where 0 is the lowest and 100% is the highest, what would that 9% be if 25% is the lowest and 75% is the highest?

What would the formula be to convert a percentage or a "normal" scale to a different scale?

Answer 1

In your scale from 0 to 100, 9 essentially represents that you are 9% of the way into the distribution:

$$9 = 0 + 9\%(100 - 0)$$

Now that your range is restricted to 25 to 75, 9% of the way into the distribution is:

$$25 + 9\%(75 - 25) = 29.5$$