Let $M$ be smooth and purely $r$-dimensional, $E$ be a vector bundle of rank $r$ over $M$, $s$ be a regular section of $E$ and $Z$ the zero scheme of $s$. Then $[Z]$ is dual to the top Chern class $c_r(E)$. When (under what conditions) can we say $Z$ consists of the top Chern number of points? Thanks!

Let $M$ be smooth and purely $r$-dimensional, $E$ be a vector bundle of rank $r$ over $M$, $s$ be a regular section of $E$ and $Z$ the zero scheme of $s$. Then $[Z]$ is dual to the top Chern class $c_r(E)$, which is set-theoretically $\mu$ points, where $\mu$ the top Chern number. When (under what conditions) can we say $Z$ consists of $\mu$ points? Or is it always true when $s$ is general enough? Thanks!