5 is exactly halfway, that's not random enough either, that's out.
2, 4, 6, 8 are even and even numbers are round and friendly and comfortable, those are out too.
9 feels too close to the boundary, it's out.
That leaves 3 and 7, and 7 is more than 3 so it's got more room for randomness in it right?
Therefore 7 is the most random number between 1 and 10.
People tend to avoid extremes, too. If you ask for a number between 1 and 10, people tend to pick something in the middle. Somehow, the ordinal values of the range seem less likely.
Additionally, people tend to avoid numbers that are in other ranges. Ask for a number from 1 to 100, and it just feels wrong to pick a number between 1 and 10. They asked for a number between 1 and 100. Not this much smaller range. You don't want to give them a number they can't use. There must be a reason they said 100. I wonder if the human RNG would improve if we started asking for numbers between 21 and 114.
So I don't think its that, 7 is still a very common "random number" here even though there is no special cultural significance to it.
Lucky Seven/Lucky Number Seven is also just a common phrase in American culture. There’s even a Wikipedia page of things called Lucky [Number] Seven. https://en.m.wikipedia.org/wiki/Lucky_7
Some sustain that 7 is the God's number, stemming from "God created the world in seven days"[1]
Also, _"According to some, 777 represents the threefold perfection of the Trinity"_ [2]
[1] https://www.wikihow.com/What-Does-the-Number-7-Mean-in-the-B...
I think you overestimate how cultural diverse western countries are when it comes to small things like this.
“Lucky Number 7” is a common phrase, there was even a popular movie that played on this, “Lucky Number Slevin” (https://m.imdb.com/title/tt0425210/). It’s one of the first numbers I’d think of as a “lucky number.”