Problem 3-05 (Algorithmic)

Brandon Lang is a creative entrepreneur who has developed a novelty soap item called Jackpot to target consumers with a gambling habit. Inside each bar of Jackpot shower soap is a single rolled-up bill of U.S. currency. The currency (rolled up and sealed in shrinkwrap) is appropriately inserted into the soap mixture prior to the cutting and stamping procedure. The distribution of paper currency (per 1000 bars of soap) is given in the following table.

Distribution of Paper Currency Prizes
Bill Denomination		Number of Bills
	$1				520
	$5				260
	$10				120
	$20				70
	$50				29
	$100				1
	Total				1000

1. What is the expected amount of money in a single bar of Jackpot soap? If required, round your answer to two decimal places. Expected value = _____________________________
2. What is the standard deviation of the money in a single bar of Jackpot soap? If required, round your answer to two decimal places. Standard deviation = _______________________________
3. How many bars of soap would a customer have to buy so that, on average, he or she has purchased four bars containing a $50 or $20 bill? If required, round up your answer to the next whole number. Number of bars of soap = ________________________________
4. If a customer buys 8 bars of soap, what is the probability that at least one of these bars contains a bill of $20 or larger? If required, round your answer to four decimal places. Probability = ______________________________________