How to interpret the Standard Error in this experiment?

[musicgold]

Homework Statement

Let's say you play a shell game. There are three shells and one of them has a coin under it. If you pick the one with a coin under it you win $10. If you pick a shell without the coin, you lose $5. You play this game 30 times.

Relevant Equations

I know that the expected value of one trial is 0. The average is (10 - 5 - 5)/3 = 0. Even with 30 trials the expeccted value is going to be 0.

The S.D. of one trial is $7.07.
But the Standard Error of 30 trials is Sqrt(30) * 7.07 = 38.72

Does the S.E. of $38.72 mean, I sould expect to win or lose up to $77.4 (2x S.E), 95% of the time?

 

[mjc123]

That is assuming the probability distribution approximates to a normal distribution. Since the number of trials is not very big, you can be more accurate by calculating the discrete binomial probabilities. I've just done this, and there is a 94.6% probability of the number of wins being from 6 to 15 inclusive, i.e. the winnings being from -$60 to +$75 inclusive. (The probability of being between ±2SE is 98.1%)