Concept explainers
The Black Gold Oil Co. is considering drilling either in Jed Clampett's back yard or his front yard. After thorough testing and analysis, they estimate that there is a
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Chapter 3 Solutions
Bundle: Mathematics: A Practical Odyssey + WebAssign Printed Access Card for Johnson/Mowry's Mathematics: A Practical Odyssey, 8th Edition, Single-Term
- The weather report says that there is a 30% chance it will rain this morning. If you take your umbrella, which cost $25,and it does not rain, there is a 20% chance that you will lose it somewhere. If you do not take your umbrella, and it does rain, you will arrive at class damp and smelly, which you would pay $10 to avoid. Should you take your umbrella?arrow_forwardAvicenna, an insurance company, offers five-year commercial property insurance policies to small businesses. If the holder of one of these policies experiences property damage in the next five years, the company must pay out $26,500 to the policy holder. Executives at Avicenna are considering offering these policies for $497 each. Suppose that for each holder of a policy there is a 2% chance they will experience property damage in the next five years and a 98% chance they will not.(If necessary, consult a list of formulas.) If the executives at Avicenna know that they will sell many of these policies, should they expect to make or lose money from offering them? How much? To answer, take into account the price of the policy and the expected value of the amount paid out to the holder. Avicenna can expect to make money from offering these policies. In the long run, they should expect to makedollars on each policy sold. Avicenna can…arrow_forwardJohn Clinton owns his own Gno-Cone business and lives 30 miles from a beach resort. The sale of Gno-Cones is highly dependent upon his location and upon the weather. At the resort, he will profit $120 per day in fair weather, $10 per day in bad weather. At home, he will profit $70 in fair weather, $55 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather. What decision is recommended by the expected monetary value criterion? [Hint: Use decision tree approach]arrow_forward
- The owner of a small firm has just purchased a personal computer, which she expects will serve her for the next two years. The owner has been told that she "must buy a surge suppressor to provide protection for her new hardware against possible surges or variations in the electrical current, which have the capacity to damage the computer. The amount of damage to the computer depends on the strength of the surge. It has been estimated that there is a 3% chance of incurring 450 dollar damage, 4% chance of incurring 250 dollar damage, and 15% chance of 75 dollar damage. An inexpensive suppressor, which would provide protection for only one surge, can be purchased. How much should the owner be willing to pay if she makes decisions on the basis of expected value? Expected Value =arrow_forwardAt a financial institution, a fraud detection system identifies suspicious transactions and sends them to a specialist for review. The specialist reviews the transaction, the customer profile, and past history. If there is sufficient evidence of fraud, the transaction is blocked. Based on past history, the specialist blocks 40 percent of the suspicious transactions. Assume a suspicious transaction is independent of other suspicious transactions. Suppose the specialist wants to know the number of suspicious transactions that will need to be reviewed until reaching the first transaction that will be blocked. (i) Define the random variable of interest and state how the variable is distributed. (ii) Determine the expected value of the random variable and interpret the expected value in context.arrow_forwardTo the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer's adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of Income, the chances of an IRS audit are increased. Data (In thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow. Adjusted Gross Income ($1,000s) Itemized Deductions ($1,000s) 22 9.6 27 9.6 32 10.1 48 11.1 65 12.5 85 16.7 120 24.5 (a) Develop a scatter diagram for these data with adjusted gross income as the independent variable. (b) Use the least squares method to develop the estimated regression equation that can be used to predict itemized deductions (in $1,000s) given the adjusted gross income (in $1,000s). (c) Predict the reasonable level of total itemized deductions (in $1,000s)…arrow_forward
- To the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer's adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow. Adjusted Gross Income ($1,000s) Itemized Deductions ($1,000s) 22 9.6 27 9.6 32 10.1 48 11.1 65 11.5 85 15.7 120 23.5 (a) Develop a scatter diagram for these data with adjusted gross income as the independent variable. 30 30 30 30 25 25 20 20 20 20 15 15 15 15 10 ... 10 10 10 ... 5. 5. 5 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 20 40 60 80 100 120 140 Adjusted Gross Income ($1,000s) Adjusted Gross Income ($1,000s) Adjusted Gross Income ($1,000s)…arrow_forwardTo the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer's adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow. Adjusted Gross Income($1,000s) Itemized Deductions($1,000s) 22 9.6 27 9.6 32 10.1 48 11.1 65 13.5 85 19.7 120 27.5 (a) Develop a scatter diagram for these data with adjusted gross income as the independent variable. (b) Use the least squares method to develop the estimated regression equation that can be used to predict itemized deductions (in $1,000s) given the adjusted gross income (in $1,000s). (Round your numerical values to three decimal…arrow_forwardTo the Internal Revenue Service, the reasonableness of total itemized deductions depends on the taxpayer's adjusted gross income. Large deductions, which include charity and medical deductions, are more reasonable for taxpayers with large adjusted gross incomes. If a taxpayer claims larger than average itemized deductions for a given level of income, the chances of an IRS audit are increased. Data (in thousands of dollars) on adjusted gross income and the average or reasonable amount of itemized deductions follow. Adjusted Gross Income($1,000s) Itemized Deductions($1,000s) 22 9.6 27 9.6 32 10.1 48 11.1 65 11.5 85 19.7 120 23.5 (a) Develop a scatter diagram for these data with adjusted gross income as the independent variable. A scatter diagram has 7 points plotted on it. The horizontal axis ranges from 0 to 140 and is labeled: Adjusted Gross Income ($1,000s). The vertical axis ranges from 0 to 30 and is labeled: Itemized Deductions ($1,000s). The points are…arrow_forward
- Joseph Bryan owns his own snow-cone business and lives 30 miles from a California beach resort. The sale of snow-cones is highly dependent on his location and on the weather. At the resort, his profit will be $120 per day in fair weather, $10 per day in bad weather. At home, his profit will be $70 in fair weather and $55 in bad weather. Assume that on any particular day, the weather service suggests a 40% chance of foul weather. Construct Joseph’s decision tree.arrow_forwardA reputable weather service issues precipitation forecasts that indicate the likelihood of measurable precipitation at a specific point during a given time period. Suppose that if a measurable amount of rain falls during the next 24 hours, a river will reach flood stage and a business will incur damages of $150,000. The weather service has indicated that there is a 35% chance of a measurable amount of rain during the next 24 hours. Complete parts a and b below. a. Construct the probability distribution that describes the potential flood damages. Sample Point Measurable amount of rain Not a measureable amount of rain Loss, x $ p(x) (Type integers or decimals. Do not round.) b. Find the firm's expected loss due to flood damage. The expected loss is $. (Type an integer or a decimal. Do not round.)arrow_forwardA reputable weather service issues precipitation forecasts that indicate the likelihood of measurable precipitation at a specific point during a given time period. Suppose that if a measurable amount of rain falls during the next 24 hours, a river will reach flood stage and a business will incur damages of $200,000.The weather service has indicated that there is a 40% chance of a measurable amount of rain during the next 24 hours. Complete parts a and b below. a. Construct the probability distribution that describes the potential flood damages. Sample Point Measurable amount of rain Not a measureable amount of rain Loss, x p(x) (Type integers or decimals. Do not round.) b. Find the firm's expected loss due to flood damage. The expected loss is (Type an integer or a decimal. Do not round.)arrow_forward
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