All $X$ are mutually independent and from normal distributions, each with its own mean and variance. If it's easier, $P(X_1 \geq X_i \forall i \in \{1, ..., n\})$ is fine although I suspect it's the same. If it matters, $n$ is between 5 and 20.

I found three similar questions:

1. The answer to this one is for only three random variables.
2. The answer to this one is for only mean 0 and variance 1.
3. I'm unsure if this one applies. If it does, I don't know how to apply it. Its top answer is for three random variables.

(This is not homework.)