Very quick question about uniform distribution.

Question

If I have a Random Variable $Y\sim U[0,60]$.
And I'm calculating $P(Y\le z)$ for $45\le z\le60$.
I'm having a little confusion if the answer is: $\frac{z-45}{15}$ OR $\frac{z}{60}$.
When I solved the question I instantly wrote $\frac{z-45}{15}$, but the solution in the book says the answer is $\frac{z}{60}$.
So it's either me having a misunderstanding of uniform distribution or the book answer is wrong.


Would appreciate any feedback, thanks in advance!

Answer 1

The uniform probability gives every result equal weight. So, say, the probability that a $Y\leq 20$ would just be $\frac {20} {60}=\frac 1 3$. The same thing will work for any $z$ in the $[0,60]$ range