In: Statistics and Probability
A creative entrepreneur has created a novelty soap called Jackpot. Inside each bar of Jackpot soap is a rolled-up bill of U.S. currency. There are 1,000 bars of soap in the initial offering of the soap. Although the denomination of the bill inside a bar of soap is unknown, the distribution of bills in these first 1,000 bars is given in the following table: Bill Denomination Number of Bills $1 520 $5 260 $10 130 $20 60 $50 29 $100 1 Total 1,000 After the sale of the original 1,000 bars of soap, Jackpot soap went viral, and the soap has become wildly popular. Production of the soap has been ramped up so that now millions of bars have been produced. However, the distribution of the bills in the soap obeys the same distribution as outlined above. On average, how many bars of soap will a customer have to buy before purchasing three bars of soap each containing a bill of at least $20 value? (Hint: Review Appendix 11.1 for descriptions of various types of probability distributions.) Round your answer to one decimal place.