To play Spin-It to Win-It, players pay $100 to spin a wheel that can land on amounts ranging from -$100 to $150. Theoretically, players can expect to lose $6.25 on average per spin with a standard deviation of $70.80. An experiment using a calculator to simulate spins found the average loss was $14 per spin with a standard deviation of $70.10, close to but not exactly matching the theoretical values. More trials may be needed to make the experimental results align more closely with the theoretical calculations.

1. Team BB

2. Instruction:
To play Spin-It to
Win-It, a player must optin by paying $100. This is
the starting bet in order to
spin the wheel. The player
must then pull the lever in
order to spin the spinner on
the machine, and whatever
the spinner lands on, he or
she wins that amount. If by
chance the spinner lands on
$0, then the player does
not win any money. The
player can stop playing
whenever he or she wants
to stop.
Spin-It to Win-It!
120
130
0
120
0
150
120
120
150
0
120
0
120
100
0
250

3. Theoretical Calculations
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Clarification: We will calculate the average profit (loss) per round that a
player incurs in a long run and its standard deviation.
Expected Value: μx = PiXi
μx = (5/16)(-100)+(6/16)(20)+(1/16)(150)(1/16)(0)+(2/16)(50)+(1/16)(30)
μx = -$6.25
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σx2 = Pi(Xi- μx)2
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σx2 = (5/16)(100+6.25)2+(6/16)(20+6.25)2+(1/16)(150+6.25)2+(1/16)(0+6.25)2+(2/16)(50+6.25)2+(1/16)(30+6.25)2
σx2 = $5012.07
σx = $70.80
A player will averagely lose $6.25 per round, and each winnings is on
average $70.80 away from the mean.

4. Experimental Calculations

According to our experiment:
We used the TI-84
Calculator to simulate
the experiment. Using
the randInt() function,
we could successfully
getthe data.
x̅ = -$14
Sx = $70.10
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http://www.youtube.com/v/BVOypPrvrP4
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5. Results
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The results show that on average a player will leave the game with a
negative profit of $14 and that the winnings results have a variation
of $70.10
The results were varied in their comparisons to the expected values.
The experimental standard deviation was very close to as it was only
$.70 below the theoretical value. But the experimental mean has a $7.75 difference from its theoretical value.
If we were to do this project over again, we would try and keep the
experimental mean closer to the theoretical mean. This could be
accomplished by having more trials. If the population side is
increased, then this would represent the long run of people; thereby
making the experimental mean closer to the theoretical mean.