Question 1134365: One state lottery has
1200 prices $1
120 prices $10
25 prices $65
5 prices $345
2 prices $1200
1 price $2700
Assuming 28,000 lottery tickets are issued and sold for $1
What is the lottery expected profit per ticket?
What is the standard deviation of profit per ticket?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! I will assume the prize of $1 means the person gains or loses nothing because they paid $1 to play. If that isn't the case, the answer will be different.
Expected value is sum of x*p(x)
=1200*0+120*9+25*64+5*344*2*1199*2699-26647*1, the losers
=-17150. This is the loss, so the profit is the positive number, which is divided by the number of tickets, or $0.6125
sd is sqrt [sum of number * deviation^2]/n-1
This is .6125^2*1200+9.6125^2*120+64.6125^2*25+344.6125^2*5+2*1199.6125^2+2699.6125^2+26647*0.3875^2/27999
notice that the last is the difference between the average profit of 0.61 and the profit of $1. The others are $1 less + the profit, taking into account the people have already paid $1.
that sum is 10904114.62
after dividing and taking the square root, the sd is $19.73
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