Looks to me like it doesn't trend toward normal. Unexpectedly it seems to skew toward the small:
Is Your Penis Bigger Than Average?
By Chris Jager -
Lifehacker Australia - May 24, 2019
"Is my penis bigger/smaller than average?" It's a question most men ask their partners at one point or another. Unfortunately, unless you're bigger than the norm (or dating a sociopath), you probably didn't receive a frank and honest answer.
The self-explanatory World Penis Data website attempts to provide a definitive answer. Here's the number you need to beat.
World Penis Data collated its results from every study on the subject that's available online. To make things more accurate, the data has been divided into objective and self-reported measurements. As you'd expect, there's a significant discrepancy between the two.
It's worth noting that these numbers are based on a collection of averages from multiple studies, rather than individual measurements. Nevertheless, the results paint a pretty comprehensive picture.
The chief takeaway is that most men think they have a six-inch erection, while scientific measurements suggest we are actually an inch shorter on average.
TLDR: If your penis length exceeds 13 centimetres while erect, you are officially longer than average.