A pawn shop is open to purchasing goods that may not have beenacquired through honest means. Every time the shop makes aquestionable transaction there is a probability that the sale getsbusted by the local police. The owner estimates that theprobability that any single transaction will be busted is 2%independent from all others. He also estimates that the net profithe makes on one transaction is well-described by a normaldistribution with average $50 with standard deviation of $15.
i. How much profit can they expect to see before the operationis busted?
ii. Find the standard deviation for total profit.
iii. A local police chief, for a monthly fee of $100, can makesure that they are not bothered as often, effectively reducingprobability of a bust on each transaction to 0.5%. Suppose thatthey do 1 questionable transaction a day. Estimate whether they canexpect to make more or less profit if they pay the bribe?
