Update2: I don't think this is exactly how I did it before, but it does appear to work.

#! perl -slw
use strict;
use List::Util qw[ sum min max ];

our $N ||= 10_000;
our $MEAN ||= 75;

sub skewedRnd {
    my( $start, $end, $skewedMean ) = @_;
    my $low = $skewedMean - $start;
    my $high = $end - $skewedMean;
    return ( rand() < 1 - ( $skewedMean / ( $end - $start ) ) )
        ? $start      + rand( $low )
        : $skewedMean + rand( $high );
}

my @values = map skewedRnd( 0, 100, $MEAN ), 1 .. $N;

printf "range 0 .. 100; Min: %f Max:%f Mean:%f \n",
    min( @values ), max( @values ), sum( @values ) / $N;

__END__
[23:52:06.41] P:\test>425761 -N=1000000 -MEAN=99
range 0 .. 100; Min: 0.003021 Max:99.999969 Mean:98.999126

[23:52:28.58] P:\test>425761 -N=1000 -MEAN=99
range 0 .. 100; Min: 5.154236 Max:99.997009 Mean:98.727916

[23:52:41.92] P:\test>425761 -N=1000 -MEAN=20
range 0 .. 100; Min: 0.029907 Max:99.995117 Mean:19.924415

[23:52:51.27] P:\test>425761 -N=1000 -MEAN=10
range 0 .. 100; Min: 0.008850 Max:97.561035 Mean:10.563889

[23:52:55.64] P:\test>425761 -N=1000 -MEAN=75
range 0 .. 100; Min: 0.144196 Max:99.998474 Mean:74.406415

[23:53:01.49] P:\test>425761 -N=1000 -MEAN=90
range 0 .. 100; Min: 1.606750 Max:99.976501 Mean:90.610480

[23:53:08.42] P:\test>425761 -N=1000 -MEAN=51
range 0 .. 100; Min: 0.049805 Max:99.974579 Mean:50.391814

[23:53:33.88] P:\test>425761 -N=1000 -MEAN=51
range 0 .. 100; Min: 0.221008 Max:99.923737 Mean:50.118810

[23:53:36.24] P:\test>425761 -N=10000 -MEAN=51
range 0 .. 100; Min: 0.001556 Max:99.998505 Mean:51.276380

[23:53:40.10] P:\test>425761 -N=100000 -MEAN=51
range 0 .. 100; Min: 0.000000 Max:99.997009 Mean:51.018693

[23:53:44.44] P:\test>425761 -N=1000000 -MEAN=51
range 0 .. 100; Min: 0.000000 Max:99.998505 Mean:50.992506
[download]

UPDATE: Below here is wrong--

#! perl -slw
use strict;

our $N ||= 10_000;
our $MEAN ||= 75;

sub skewedRnd {
    my( $start, $end, $skewedMean ) = @_;
    my $skewFactor = $skewedMean - ( ( $end - $start ) / 2 );
    
    return $start + rand( $end - $start ) 
        + rand( $skewFactor * 2 );
}

my $total;
$total += skewedRnd( 0, 100, $MEAN ) for 1 .. $N;

print $total / $N;

__END__
[21:56:57.38] P:\test>425761 -N=100000 -MEAN=75
75.060163192749

[21:57:13.74] P:\test>425761 -N=100000 -MEAN=32
32.1195869335938
[download]

I'll let the math guys pick it apart, and offer it on the basis that it is simple, understandable and served my purpose. Maybe it will serve yours too.