Update:

So, I've worked out that because of the skew of the distribution, the "mean" that I have been specifying is actually the mode. When I grouped the random numbers generated in the example and grouped them, the mode is 225,000 or there abouts.

So, all I now need to do, I think(!), is generate a formula that will take my desired mean, and convert it into a mode that when plugged in to the mapping that I stated, give me a set of data with my "desired mean" as the mean...

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