What is the relationship between Noise Power in a Band-Limited White Noise block and the Variance in a Random Number block?

For example, if we use 0.1 for the former and 100 for the latter, with a sampling time of 0.001, we get the same results (besides the band limitation, which is not apparent here, but can be seen if we do a PSD; it will have a small effect, but let's forget about it).

After some numerical experiments, I guess that it is:

But what is reason/formula behind it?

I went over the documentation and googled it, but I do not find a simple formula to compute one from the other, and I feel this should be pretty simple.

Thanks

PS: the motivation is to translate specs from another software into Matlab.

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