Brandon Lang is creative entrepreneur ho has developed a novelty soap item calle

Question

Brandon Lang is creative entrepreneur ho has developed a novelty soap item called Jackpot to target consumers with a gambling habit. Inside each ber of Jackpot shower soap is a single rolled up bof u 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 currency. The currency rolled up and Distribution of Paper Currency Prizes Bill Denomination Number of Bills 570 210 140 50 27 S1 10 s20 50 $100 Total 1000 a. What is the expected amount of money in a single bar of Jackpot soap? If required, round your answer to two decimal places. Expected velue - b. What is the standard devlation of the money In a single bar of Jackpot soap? If required, round your answer to two decimal places. Standard devlation- c. How many bars of soap would customer have to buy so that, on average, he or she has purchas d four bars containing $10 or $100 bill? If required, round up your answer to the next whole number Number of bars of soap d. If a customer buys 7 bars of soap, what is the probability that at least one of these bars contains a bill of s20 or larger? if required, round your answer to four decimal places. Probability

Explanation / Answer

= (105.1711)1/2 = 10.255%

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(x) (p) (xp) Bill Denomination No. of Bills Probability $1 570 0.57 0.57 $5 210 0.21 1.05 $10 140 0.14 1.4 $20 50 0.05 1 $50 27 0.027 1.35 $100 3 0.003 0.3 1000 5.67 The Expected Amount of Money(Mean) 5.67 Solution (b) The Calculation of standard deviation (x) (x - mean) (x - mean)2 Probability Prob*(x-mean)2 Bill Denomination $1 -4.67 21.8089 0.57 12.43107 $5 -0.67 0.4489 0.21 0.094269 $10 4.33 18.7489 0.14 2.624846 $20 14.33 205.3489 0.05 10.26745 $50 44.33 1965.1489 0.027 53.05902 $100 94.33 8898.1489 0.003 26.69445 Total 105.1711 Therefore the variance is 105.1711 Now the standard Deviation is (Variance)2

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