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1. 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 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. Distribution of Paper Currency Prizes Bill Denomination Number of Bills $1 $5 $10 $20 $50 $100 520 260 120 70 29 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 wvould a customer have to buy so that, on average, he or she has purchased three bars containing a $50 or $100 bill? c.

1. 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 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. Distribution of Paper Currency Prizes Bill Denomination Number of Bills $1 $5 $10 $20 $50 $100 520 260 120 70 29 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 wvould a customer have to buy so that, on average, he or she has purchased three bars containing a $50 or $100 bill? c.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Page < 17 of 18 between occurrences Problem Exercises: 1. 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 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. Distribution of Paper Currency Prizes Bill Denomination Number of Bills 520 260 120 S5 $10 S20 $50 S100 29 Total 1000 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? a.
Transcribed Image Text:Page < 17 of 18 between occurrences Problem Exercises: 1. 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 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. Distribution of Paper Currency Prizes Bill Denomination Number of Bills 520 260 120 S5 $10 S20 $50 S100 29 Total 1000 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? a.
Page 18 of 18 ZOOM + 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? 2. In 2003, the average stock price for companies making up the S&P 500 was $30, and the standard deviation was $8.20 (BusinessWeek, Special Annual Issue. Spring 2003). Assume the stock prices are normally distributed. a. What is the probability that a company will have a stock price of at least $40? b. What is the probability that a company will have a stock price no higher than $20? c. How high does a stock price have to be to put a company in the top 10%%?
Transcribed Image Text:Page 18 of 18 ZOOM + 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? 2. In 2003, the average stock price for companies making up the S&P 500 was $30, and the standard deviation was $8.20 (BusinessWeek, Special Annual Issue. Spring 2003). Assume the stock prices are normally distributed. a. What is the probability that a company will have a stock price of at least $40? b. What is the probability that a company will have a stock price no higher than $20? c. How high does a stock price have to be to put a company in the top 10%%?
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