what is binorminal distribution and what it is for.

this is simple example

You have one coin.
You and your freind will work for night duty.
According to the results of coin.
if face: your duty.
if back: friend duty.

for 100 times,
if 50 times face -- both will think it's fair or the coin is normal.

how about 40 times, do you think the coin is normal?
how about 20 times, do you think the coin is normal?

you can get the possibility by this excel sheet.