We can have fun speculating whether there are any a priori reasons why women should be normal & men lognormal
At the level of basic genetics we might expect there to be greater variations between men than between women because of the X & Y chromosomes. Any mutation in an X chromosome gene might be 'corrected' in a female by the copy provided by the other parent. And of course women do not have a Y chromosome at all to add variation
But if the basic distributions, not just the mean & variances, are different then that suggests that the processes by which the variations - or errors - are differnet [leave that typo - Ed]
Under the Normal Law of error myriad sources of error affect the deviation from the true, mean value of any observation, & all these small individual effects add together. But under the lognormal distribution the errors, or differences, will multiply themselves up
To take a crude example, if income depends on education, height & good looks, then a man lucky enough to possess a high score on all 3 will have a much greater advantage than a woman who is similarly lucky. He will get the compound interest, she will only get simple interest
