Another type of carnival or arcade game is a spinning wheel game. imagine that someone playing a spinning wheel
game earns points (payoff) as follows for each spin:
 you gain 2 points 50% of the time.
 you lose 3 points 25% of the time.
 you neither gain nor lose any points 25% of the time.
the results of each spin are added to one another, and the object is for a player to accumulate 5 or more points.
negative total point values are possible.
a. develop a model of a spinning wheel that would reflect the probabilities and point values.
b. compute where represents the number of points earned in a given spin.
c. based on your computation, how many spins on average do you think it might take to reach 5 points?
d. use the spinning wheel you developed in part (a) (or some other randomization device) to take a few spins.
see how many spins it takes to reach 5 or more points. comment on whether this was fewer spins, more
spins, or the same number of spins you expected in part (c).
e. let represent the number of spins needed to reach 5 or more points (like the number of spins it took you to
reach 5 points in part ( and repeat the simulation process from part (d) many times. record on a dot plot
the various values of you obtain. after several simulations, comment on the distribution of