wilson score interval possible results range

Question

This question is about Wilson score confidence interval (see here for explanation).

I do not completly understand the scoring equation:
_{(source: evanmiller.org)}

But.. I just need to know what is the range of the possible results.

I need to give 1 out of 3 medals to the user accordig to the rate.

(I have recipes created by users, can do "Like" on them, and accordingly I calculate the rate of the recipe. User rate is calculated according to his recipes rates.)

Thanks Yoav

Answer 1

The equation is returning bounds on a probability, so the range should be greater than or equal to zero and less than or equal to 1.