Question

Suppose that in a casino, a certain slot machine pays out an average of Php 15, with a standard deviation of Php 5,000. Every play of the game costs a gambler Php 20.

a. Why is the standard deviation so large?

b. If your parent decides to play with this slot machine 5 times, what are the mean and standard deviation of the casino's profit?

c. If the gamblers play with this slot machine 1000 times in a day, what are the mean and standard deviation of the casino's profits?

Answer 1

$a:\\You\,\,may\,\,win\,\,much\,\,or\,\,nothing, the\,\,range\,\,is\,\,wide\\b:\\EX_1=20-15=5\\EX=E\sum_{1\leqslant i\leqslant 5}{X_i}=5EX_1=5\cdot 5=25\\DX=D\sum_{1\leqslant i\leqslant 5}{X_i}=5DX_1=5\cdot 5000^2=1.25\times 10^8\\\sigma X=\sqrt{DX}=\sqrt{1.25\times 10^8}=11180.3\\c:\\EX=E\sum_{1\leqslant i\leqslant 1000}{X_i}=1000EX_1=1000\cdot 5=5000\\DX=D\sum_{1\leqslant i\leqslant 1000}{X_i}=1000DX_1=1000\cdot 5000^2=2.5\times 10^{10}\\\sigma X=\sqrt{DX}=\sqrt{2.5\times 10^{10}}=158114$