Question

230 5. Brandon Lang is a creative entrepreneur who has developed a novelty soap item called Jack- pot 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 shrink-wrap) 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. $1 Distribution of Paper Currency Prizes Bill Denomination Number of Bills 520 $5 260 $10 120 $20 70 $50 29 $100 Total 1000 a. What is the expected amount of money in a single bar of Jackpot soap? b. What is the standard deviation of the money in a single bar of Jackpot soap? How many bars of soap would a customer have to buy so that, on average, he or she has purchased three bars containing a $50 or $100 bill? c.

Answer 1

Solution - information as Number of bill From the given Bill Denomination $1 $5 $10 520 260 120 $20 $50 29 $100 Total loro a Expected amount of money in a single bar of jackpot soap Bill Denomination (x) No. of bill (P(x)) xp(xi) 0.52 0.26 0.52 1.3 0-12 o.oto o-ool 0. Total Exp(xi) = 5.52 Hence, the expected value is : [5.52)

b) Std. der. of of jackpot single bar the money in a soap. P(xi) lai-E (2) / lxi-E(x) IP(xi) 0.52 20.43 10.62 o G - 20.02 2.4084 e 0.07 209.67 § 9 0.02 1978.47 14.6764 39.5694 8.92647 8926.4704 Total 1.000 76.2202 sta. dev. = Jlai - E (x)} P (mi) J 76. 2702 = 8.73328 - 18.73) Let z denoty the number of bars that contains so er zo bill That is: 50429 + 20x70 bill now, there are so that contain the $50 & $20 bill $50 31 100 = 30

probability - loro = 0.003 0.03 so, E(2) = np. = nxo-003 Qoo 0.03 0.03 n =100