A slot machine at a casino costs $2.00 to play. It is designed such that each play of the game then has a mean payout amount of $1.77, with a standard deviation of $87. Let us suppose that the slot machine is played exactly 800 times in a day.
a) If the machine is played 800 times in a day, what are the mean and standard deviation of the casino's total profits from this slot machine for that day?
b) Based on anecdotal (casual) observations, the casino owner is concerned that a lot of people seem to be winning the jackpot on this slot machine. With a large enough sample size, the casino's total profits for 800 plays of the slot machine are approximately normally distributed. Based on the mean and standard deviation calculated in part (a), what is the probability that this slot machine will lose the casino more than $5,000 in a given day?
(In other words, what is the probability that this slot machine's profits are below -5,000?)
c) Suppose that on a given day, this slot machine loses the casino more than $5,000. Based on your answer to part (b), would you consider this to be a RARE or UNLIKELY occurrence? Explain.