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?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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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