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 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 procedurel. The distribution of paper currency (per 1000 bars of soap) is given in the following table
Distribution of Paper Currency
Bill Denomination Number of Bills
a. What is the expected amount of money in a single bar of Jackpot soap?
b. What is the standard deviation 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 $50 or $100 bill?
d. If a customer buys 8 bars of soap, what is the probability that at least one of these bars contains a bill of $20 or larger?
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a. Computation of expected amount of money in a single bar of Jackpot soap:
The number of bills for $100 denomination is considered as 1 so that the total would be 1000.
The expected amount of money in a single bar of Jackpot soap is obtained as 5.97, from the calculation given below:
b. Computation of standard deviation in a single bar of Jackpot soap:
The standard deviation in a single bar o...
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