Problem 3-05 (Algorithmic) Brandon Lang is a creativeentrepreneur who has developed a novelty soap item called Jackpotto target consumers with a gambling habit. Inside each bar ofJackpot shower soap is a single rolled-up bill of U.S. currency.The currency (rolled up and sealed in shrinkwrap) is appropriatelyinserted into the soap mixture prior to the cutting and stampingprocedure. The distribution of paper currency (per 1000 bars ofsoap) is given in the following table. Distribution of PaperCurrency Prizes Bill Denomination Number of Bills $1 500 $5 250 $10150 $20 50 $50 49 $100 1 Total 1,000 (a) What is the expectedamount of money in a single bar of Jackpot soap? If required, roundyour answer to two decimal places. Expected value = (b) What is thestandard deviation of the money in a single bar of Jackpot soap? Ifrequired, round your answer to two decimal places. Standarddeviation = (c) How many bars of soap would a customer have to buyso that, on average, he or she has purchased four bars containing a$10 or $20 bill? If required, round up your answer to the nextwhole number. Number of bars of soap = (d) If a customer buys 9bars of soap, what is the probability that at least one of thesebars contains a bill of $20 or larger? If required, round youranswer to four decimal places. Probability =