# Page:Popular Science Monthly Volume 12.djvu/735

 half the time within 0.477 ${\displaystyle {\sqrt {\tfrac {2p(1-p)}{s}}}}$ 9 times out of 10 within 1.163 ${\displaystyle {\sqrt {\tfrac {2p(1-p)}{s}}}}$ 99 times out of 100 within 1.821 ${\displaystyle {\sqrt {\tfrac {2p(1-p)}{s}}}}$ 999 times out of 1,000 within 2.328 ${\displaystyle {\sqrt {\tfrac {2p(1-p)}{s}}}}$ 9,999 times out of 10,000 within 2.751 ${\displaystyle {\sqrt {\tfrac {2p(1-p)}{s}}}}$ 9,999,999,999 times out of 10,000,000,000 within 4.77 ${\displaystyle {\sqrt {\tfrac {2p(1-p)}{s}}}}$