babloo,
Ok - not knowing the reason you are supposed to do this without a module I didn't spend a lot of time trying to come up with a scientific solution. I did find that the following code did work surprisingly well for the requirements you specified: 
#!/usr/bin/perl -w
use strict;

my $desired_mean = 250;
my $desired_deviation = 20;
my $total = 1000;

my @numbers;

gen_numbers(\@numbers, $desired_mean, $desired_deviation, $total);

sub gen_numbers {
   my ($array_ref, $mean, $deviation, $total) = @_;
   my $offset = $deviation * 1.75;
   my $low = $mean - $offset;
   my $high = $mean + $offset;
   for (0 .. $total) {
       my $number;
       while (1) {
            $number = int(rand($high)) + 1;
            last if ($number >= $low && $number <= $high);
       }

       push @{$array_ref} , $number
   }
}

my $sum;
$sum += $_ for @numbers;

my $mean = $sum / $total;

my $scratch;
for (@numbers) {
   $scratch += (($_ - $mean) * ($_ - $mean));
}

my $standard_deviation = sqrt($scratch / ($total - 1));

print "Desired Mean:  $desired_mean\n";
print "Mean:  $mean\n";
print "\n";
print "Desired Standard Deviation:  $desired_deviation\n";
print "Standard Deviation:  $standard_deviation\n";
__END__
Desired Mean:  250
Mean:  250.06707

Desired Standard Deviation:  20
Standard Deviation:  19.9571308028178

[download]

I doubt seriously it will work for anything other than 20 for a standard deviation since I used the fact that 3 standard deviations from the mean accounts for 99.7% in a normal distribution. I then fudge factored the remaining .3%.

Cheers - L~R

In reply to Re: how can i generate random numbers with predefined mean and standard deviation by Limbic~Region
in thread how can i generate random numbers with predefined mean and standard deviation by Anonymous Monk

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