# 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 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                              Distribution of Paper Currency Prtizes                    Bill Denomination                      Number of Bills                              \$1                                                520                              \$5                                                260                              \$10                                              120                                                 \$20                                                70                              \$50                                                29                              \$100                                               1                              Total                                        1000a. 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?c. 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?d. If a customer buys 8 bars of soap, wht is the probability that at least one of these bars contains a bill of \$20 or larger?

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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 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

Distribution of Paper Currency Prtizes

Bill Denomination                      Number of Bills

\$1                                                520

\$5                                                260

\$10                                              120

\$20                                                70

\$50                                                29

\$100                                               1

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?

c. 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?

d. If a customer buys 8 bars of soap, wht is the probability that at least one of these bars contains a bill of \$20 or larger?

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Step 1

Hello there! there are more than three subparts in the question. According to our policies we cannot answer more than three sub parts in one question. So please find the solution for a,b,c parts of the question. If you have doubts in remaining part of the question kindly make a new request, mentioning the part in which you need help.

Given data and calculation for probability, mean and standard deviation is shown below

Step 2

c) no of bars of soap  a customer have to buy so that, on average, he or she has ...

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