Can somebody help refresh my statistical knowledge that I have not used 
for over twenty years?

I am trying to figure out the formula | algorithm to create random 
numbers that will follow a specific probability distribution.  The 
distribution I want is asymmetrical.  There are more numbers on the 
right of the mean then the left.  I would like the mean to be 175 with a 
1 standard deviation
of 50 to 300.  The tricky part, I think, is that the overall 
distribution is 20 to 1000.

Does that make sense?  Did I just completely mangle and abuse the 
terminology?
I'll attempt to draw an ASCII art representation in case that helps.

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. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2          5        1        3                                      1
0          0        7        0                                      0
                     5        0                                      0
                                                                     0


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