Does probabibility depend on mean or standard deviation?

It depends on both. As a simple example, take X to be a constant random variable, say X(w) = c for every point w in the sample space. Then…
Have you actually tried doing what it says, and picking pairs of values to test the computation?  That should tell you exactly what the answer is.
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You were asked to experiment in order to form that hypothesis. I mean, you might have your guess, but the problem specifically asks you to vary μ and σ and see the effect.

I assume that this is for a particular probability distribution. If not, pick one.
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