You probably missed that your question was put at How do I get random numbers that follow standard distribution? in Categorized Questions and Answers.

There are several answers there, including mine at Re: How do I get random numbers that follow standard distribution?.

UPDATE
After talking with you I found that you have two rather irritating conditions. You cannot easily install modules, and you want to skew the output. Here is some sample code that gives you an idea how to do that, but I am warning you that it will take a lot of playing around to get this to produce what you want...

my @weights = qw(0.5 1 2);
my @random = sort {$a <=> $b} map{rand()} 0..$#weights;
my $tot;
foreach (0..$#weights) {
    $tot += $random[$_] * $weights[$_];

}
print $tot;
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