[spappal]

P(simultaneously within middle 50 % of n independent distributions) = 0.5^n = 2^(-n), like my parent comment says.

But interestingly, every relevant comment here either got something wrong about the final frequency or percentage, or corrected the wrong thing. (Parent comment, grandparent, 2 aunts and 1 cousin.)

0.5^10 = 2^-10 = 1/(2^10) = 1/1024 [i.e. exactly 1 person per 1024] ~= 0.00097656 ~= 0.09766 %.

[saeranv]

Hah, you are correct. I even had access to numpy and still managed to get this wrong.