4. After realizing that you're almost destined to lose money in Vegas, you decide to go into the casino of the Bellagio to tempt your fate. A flashy slot machine with loud music and bright colors catches your eye - you gravitate to it. Suppose it is known that the mean payout for a single bet (pull) on this machine is $1 with a standard deviation of $0.50, and it costs $2 per pull.

a) If you sat at this machine and made 100 bets (pulls): (i) Would the distribution of your average payout be approximately Normal? Explain. (ii) Would this change if you were to make only 10 bets?

b) Assuming you do make 100 bets on this machine, what is the probability that you will walk away from the machine having netted a profit?

c) Now, suppose the mean payout for a single bet on this machine is known to be approximately Normal. (i) What is the probability that you'd walk away with a profit after 1 bet? (ii) What number of bets should you make to expect the most profit?