I am confused by this question:
A casino knows that people play the slot machines in hopes of hitting the jackpot, but the most of them lose their dollar. Suppose a certain machine pays out an average of 0.92, with a standard deviation of 120.
The question then is: If somebody plays five times, what is the standard deviation of the casino's profit?
The right answer, supposedly, is to divide the std by $\sqrt5$. I can see how, over consecutive attempts, the deviance from the mean would get smaller, but I am rather confused by the logic of the whole question – would that then mean that over time the standard deviation gets to zero? What does then the 120 even mean – standard deviation of what? I suppose I need to clear a general confusion, as I am not quite sure what is the right question to ask.
Thanks for any help.
Best Answer
This involves a random variable...that is, a real-valued function defined on the space of outcomes. In this case, a person plays five times, a certain outcome happens, and a real number (the casino's profit) emerges.
A random variable has a mass function, which gives the probability that the random variable will take a certain value. From this, we can define things such as the mean, the standard deviation, etc.
In this case, the random variable is a sum of five independent identically distributed random variables. The individual variables are the ones you have information on.