Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
6th Edition
ISBN: 9780321914620
Author: Jeffrey O. Bennett, William L. Briggs
Publisher: PEARSON
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Textbook Question
Chapter 3.C, Problem 1QQ
The $5.6 trillion surplus that government economists had projected in 2001 never materialized because the people who made this projection
a. didn’t really understand how the government budget works.
b. based in on assumptions about the future economy that turned out to be untrue.
c. made basic errors in their calculations.
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(b) An otherwise fair six-sided die has been tampered with in an attempt to
cheat at a dice game. The effect is that the 1 and 6 faces have a
different probability of occurring than the 2, 3, 4 and 5 faces.
Let θ be the probability of obtaining a 1 on this biased die. Then the
outcomes of rolling the biased die have the following probability mass
function.
Table 1 The p.m.f. of outcomes of rolls of a biased die
Outcome 1 2 3 4 5 6
Probability θ
1
4
(1 − 2θ)
1
4
(1 − 2θ)
1
4
(1 − 2θ)
1
4
(1 − 2θ) θ
(i) By consideration of the p.m.f. in Table 1, explain why it is
necessary for θ to be such that 0 < θ < 1/2. [2]
(ii) The value of θ is unknown. Data from which to estimate the value
of θ were obtained by rolling the biased die 1000 times. The result
of this experiment is shown in Table 2.
Table 2 Outcomes of 1000 independent rolls of a biased die
Outcome 1 2 3 4 5 6
Frequency 205 154 141 165 145 190
Show that the likelihood of θ based on these data is
L(θ) = C θ395 (1 − 2θ)
605
,…
Problem: The probability density function of a random variable is given by the exponential
distribution
Find the probability that
f(x) = {0.55e-0.55 x 0 < x, O elsewhere}
a. the time to observe a particle is more than 200 microseconds.
b. the time to observe a particle is less than 10 microseconds.
How to solve it explain it step by step please
Chapter 3 Solutions
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Ch. 3.A - Prob. 1QQCh. 3.A - The population of a town increases from 50,000 to...Ch. 3.A - Suppose the value of a home changed by -20% over...Ch. 3.A - Emily scored 50% higher on the SAT than Joshua....Ch. 3.A - The price of a movie ticket increased from $10 to...Ch. 3.A - Your receipt shows that you paid $47.96 for a new...Ch. 3.A - Consider the statement “The interest rate on auto...Ch. 3.A - A friend has a textbook that originally cost $150....Ch. 3.A - You currently earn $1000 per month, but you are...Ch. 3.A - During high school, Elise won 30% of the swim...
Ch. 3.A - Describe the three basic uses of percentages. Give...Ch. 3.A - Distinguish between absolute and relative change....Ch. 3.A - Distinguish between absolute and relative...Ch. 3.A - Explain the difference between the key words of...Ch. 3.A - Explain the difference between the terms percent...Ch. 3.A - 6. Give an example to explain why, in general, it...Ch. 3.A - In many European countries, the percentage change...Ch. 3.A - The price of tuition has tripled since my parents...Ch. 3.A - Prob. 9ECh. 3.A - I’ve decreased my caloric intake by 125% which has...Ch. 3.A - If you earn 20% more than I do, then I must earn...Ch. 3.A - If they raise taxes by 10% every year, in a decade...Ch. 3.A - We found that these rare cancers were 700% more...Ch. 3.A - Prob. 14ECh. 3.A - The rate of return on our fund increased by 50%,...Ch. 3.A - My bank increased the interest rate on my savings...Ch. 3.A - Prob. 17ECh. 3.A - Prob. 18ECh. 3.A - Prob. 19ECh. 3.A - Prob. 20ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 22ECh. 3.A - Prob. 23ECh. 3.A - Prob. 24ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 27ECh. 3.A - Prob. 28ECh. 3.A - Fractions, Decimals, Percentages. Express the...Ch. 3.A - Prob. 30ECh. 3.A - Prob. 31ECh. 3.A - Prob. 32ECh. 3.A - Prob. 33ECh. 3.A - Prob. 34ECh. 3.A - Prob. 35ECh. 3.A - Prob. 36ECh. 3.A - Prob. 37ECh. 3.A - Prob. 38ECh. 3.A - Compare the following pairs of numbers A and B in...Ch. 3.A - Compare the following pairs of numbers A and B in...Ch. 3.A - Prob. 41ECh. 3.A - Prob. 42ECh. 3.A - Percentages as Fractions. In the following...Ch. 3.A - Prob. 44ECh. 3.A - Percentages as Fractions. In the following...Ch. 3.A - Prob. 46ECh. 3.A - Prob. 47ECh. 3.A - Prob. 48ECh. 3.A - Salary Comparisons. Clint’s salary increased from...Ch. 3.A - Population Comparison. Between the 2010 U.S....Ch. 3.A - Percentage change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Change. Find the absolute change and...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Percentage Comparisons. Complete the following...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Of versus More Than. Fill in the blanks in the...Ch. 3.A - Prob. 64ECh. 3.A - Prices and sales. Fill the blanks in the following...Ch. 3.A - Prob. 66ECh. 3.A - Prices and sales. Fill the blanks in the following...Ch. 3.A - Prob. 68ECh. 3.A - Prob. 69ECh. 3.A - Prob. 70ECh. 3.A - Prob. 71ECh. 3.A - Prob. 72ECh. 3.A - Care in Wording. Assume that 30% of city employees...Ch. 3.A - Ambiguous News. The average annual precipitation...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Prob. 76ECh. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Prob. 78ECh. 3.A - Prob. 79ECh. 3.A - Prob. 80ECh. 3.A - Shifting Reference Value. State whether the...Ch. 3.A - Prob. 82ECh. 3.A - Prob. 83ECh. 3.A - Prob. 84ECh. 3.A - Prob. 85ECh. 3.A - Prob. 86ECh. 3.A - Is it Possible? Determine whether the following...Ch. 3.A - Prob. 88ECh. 3.A - Average Percentages. You are a teacher. Your...Ch. 3.A - Prob. 90ECh. 3.A - Prob. 91ECh. 3.A - Prob. 92ECh. 3.A - Prob. 93ECh. 3.A - Prob. 94ECh. 3.A - Prob. 95ECh. 3.A - Prob. 96ECh. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - 95-100 Solving Percentage Problems. Solve the...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Solving Percentage Problems. Solve the following...Ch. 3.A - Percentages in the News. Answer the question that...Ch. 3.A - Prob. 102ECh. 3.A - Percentages in the News. Answer the question that...Ch. 3.A - Prob. 104ECh. 3.A - Prob. 105ECh. 3.A - Prob. 106ECh. 3.A - Prob. 107ECh. 3.A - 108. Stock Market Losses.
a. The largest...Ch. 3.A - Percentages. Find three recent news reports that...Ch. 3.A - Percentage Change. Find a recent news report that...Ch. 3.A - Prob. 111ECh. 3.B - Prob. 1QQCh. 3.B - Prob. 2QQCh. 3.B - Prob. 3QQCh. 3.B - 4. You are asked to estimate the total amount of...Ch. 3.B - 5. You are wondering how many dollar bills you’d...Ch. 3.B - 6. You are given some data and asked to calculate...Ch. 3.B - Prob. 7QQCh. 3.B - Prob. 8QQCh. 3.B - Prob. 9QQCh. 3.B - A lottery ticket on which the odds of winning are...Ch. 3.B - Briefly describe scientific notation. How is it...Ch. 3.B - Prob. 2ECh. 3.B - Prob. 3ECh. 3.B - Explain how we can use comparisons to put numbers...Ch. 3.B - 5. Describe three common ways of expressing the...Ch. 3.B - 6. Explain how we can use scaling to put numbers...Ch. 3.B - 7. Suppose that the Sun were the size of a...Ch. 3.B - 8. Describe several ways of putting each of the...Ch. 3.B - Prob. 9ECh. 3.B - I’ve seen about commercials on TV.Ch. 3.B - I live in an apartment building that is 200 feet...Ch. 3.B - In total, Americans spend about a billion dollars...Ch. 3.B - After a recent NFL football game, the star player...Ch. 3.B - The CEO of the company earned more money last year...Ch. 3.B - Prob. 15ECh. 3.B - Prob. 16ECh. 3.B - Prob. 17ECh. 3.B - Review of Scientific Notation. In the following...Ch. 3.B - Prob. 19ECh. 3.B - Prob. 20ECh. 3.B - Prob. 21ECh. 3.B - Prob. 22ECh. 3.B - Using Scientific Notation. Rewrite the following...Ch. 3.B - Prob. 24ECh. 3.B - 23-26: Using Scientific Notation. Rewrite the...Ch. 3.B - Prob. 26ECh. 3.B - Prob. 27ECh. 3.B - Prob. 28ECh. 3.B - 29-32: Perspective Through Estimation. Use...Ch. 3.B - Prob. 30ECh. 3.B - Prob. 31ECh. 3.B - Prob. 32ECh. 3.B - Prob. 33ECh. 3.B - Prob. 34ECh. 3.B - Prob. 35ECh. 3.B - 33-40: Order of Magnitude Estimates. Make order of...Ch. 3.B - Prob. 37ECh. 3.B - Prob. 38ECh. 3.B - Prob. 39ECh. 3.B - Prob. 40ECh. 3.B - Prob. 41ECh. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - 41-48: Energy Comparisons. Use Table 3.1 to answer...Ch. 3.B - Prob. 45ECh. 3.B - Prob. 46ECh. 3.B - Prob. 47ECh. 3.B - Prob. 48ECh. 3.B - Prob. 49ECh. 3.B - Scale Ratios. Find the scale ratios for the...Ch. 3.B - Scale Ratios. Find the scale ratios for the...Ch. 3.B - Prob. 52ECh. 3.B - Scale Model Solar System. The following table...Ch. 3.B - 54. Interstellar Travel. The fastest spaceships...Ch. 3.B - Prob. 55ECh. 3.B - Prob. 56ECh. 3.B - Prob. 57ECh. 3.B - Making Numbers Understandable. Restate the...Ch. 3.B - Prob. 59ECh. 3.B - Making Numbers Understandable. Restate the...Ch. 3.B - Prob. 61ECh. 3.B - Prob. 62ECh. 3.B - Prob. 63ECh. 3.B - Prob. 64ECh. 3.B - Cells in the Human Body. Estimates of the number...Ch. 3.B - Emissions. For every gallon of gasoline burned by...Ch. 3.B - Prob. 67ECh. 3.B - Wood for Energy? A total of about 180,000...Ch. 3.B - Stellar Corpses: White Dwarfs and Neutron Stars. A...Ch. 3.B - Until the Sun Dies. It took 65 million years from...Ch. 3.B - Personal Consumption. The Bureaus of Economic...Ch. 3.B - Sampling Problems. Sampling techniques can be used...Ch. 3.B - Prob. 73ECh. 3.B - 72 – 75 : Sampling Problems. Sampling techniques...Ch. 3.B - Sampling Problems. Sampling techniques can be used...Ch. 3.B - 76. Energy Comparisons. Using data available from...Ch. 3.B - Prob. 77ECh. 3.B - Prob. 78ECh. 3.B - Prob. 79ECh. 3.B - Prob. 80ECh. 3.B - Prob. 81ECh. 3.B - Putting Numbers in Perspective. Find at least two...Ch. 3.B - Prob. 83ECh. 3.C - The $5.6 trillion surplus that government...Ch. 3.C - Under the standard rules for counting significant...Ch. 3.C - Under the standard rules for counting significant...Ch. 3.C - You are trying to measure the outside temperature...Ch. 3.C - You are trying to measure the outside temperature...Ch. 3.C - A testing service makes a error that causes all...Ch. 3.C - A testing service makes an error that causes all...Ch. 3.C - A digital scale shows that you weigh 112.7 pounds,...Ch. 3.C - At a particular moment, the U.S. National Debt...Ch. 3.C - Prob. 10QQCh. 3.C - Prob. 1ECh. 3.C - Prob. 2ECh. 3.C - Prob. 3ECh. 3.C - Distinguish between accuracy and precision. Give...Ch. 3.C - Why can it be misleading to give measurements with...Ch. 3.C - Prob. 6ECh. 3.C - Next year’s federal deficit will be $675.34...Ch. 3.C - In many developing nations, official estimates of...Ch. 3.C - I weigh 110.3627 pounds.Ch. 3.C - The 2013 presidential inauguration brought 925,500...Ch. 3.C - Wilma used a yard stick to measure the length of...Ch. 3.C - More precision is useless if the measurement is...Ch. 3.C - 13. A $1 million error may sound like a lot, but...Ch. 3.C - Prob. 14ECh. 3.C - Prob. 15ECh. 3.C - Review of Rounding. In the following exercises,...Ch. 3.C - Counting Significant Digits. State the number of...Ch. 3.C - Counting Significant Digits. State the number of...Ch. 3.C - Counting Significant Digits. State the number of...Ch. 3.C - Prob. 20ECh. 3.C - 17-28: Counting Significant Digits. State the...Ch. 3.C - Prob. 22ECh. 3.C - Prob. 23ECh. 3.C - Prob. 24ECh. 3.C - Prob. 25ECh. 3.C - Prob. 26ECh. 3.C - Prob. 27ECh. 3.C - 17-28: Counting Significant Digits. State the...Ch. 3.C - Prob. 29ECh. 3.C - Rounding with Significant Digits. Carry out the...Ch. 3.C - Prob. 31ECh. 3.C - Prob. 32ECh. 3.C - Prob. 33ECh. 3.C - Prob. 34ECh. 3.C - Source of Error. Describe possible source of...Ch. 3.C - Prob. 36ECh. 3.C - Source of Error. Describe possible source of...Ch. 3.C - Source of Error. Describe possible source of...Ch. 3.C - Prob. 39ECh. 3.C - 35-42: Source of Error. Describe possible source...Ch. 3.C - Prob. 41ECh. 3.C - Source of Error. Describe possible source of...Ch. 3.C - Tax Audit. A tax auditor reviewing a tax return...Ch. 3.C - AIDS Epidemic. Researchers studying the...Ch. 3.C - Prob. 45ECh. 3.C - Cutting Lumber. A lumber yard employee cuts 30...Ch. 3.C - Prob. 47ECh. 3.C - Absolute and Relative Errors. Find the absolute...Ch. 3.C - Absolute and Relative Errors. Find the absolute...Ch. 3.C - Absolute and Relative Errors. Find the absolute...Ch. 3.C - Prob. 51ECh. 3.C - Prob. 52ECh. 3.C - Prob. 53ECh. 3.C - 47-54: Absolute and Relative Errors. Find the...Ch. 3.C - Prob. 55ECh. 3.C - Accuracy and Precision. For each pair of...Ch. 3.C - Prob. 57ECh. 3.C - Accuracy and Precision. For each pair of...Ch. 3.C - Combining Numbers. Use the appropriate rounding...Ch. 3.C - Combining Numbers. Use the appropriate rounding...Ch. 3.C - Combining Numbers. Use the appropriate rounding...Ch. 3.C - Prob. 62ECh. 3.C - Prob. 63ECh. 3.C - 59-66: Combining Numbers. Use the appropriate...Ch. 3.C - Combining Numbers. Use the appropriate rounding...Ch. 3.C - Prob. 66ECh. 3.C - Prob. 67ECh. 3.C - Prob. 68ECh. 3.C - Prob. 69ECh. 3.C - Prob. 70ECh. 3.C - Prob. 71ECh. 3.C - Prob. 72ECh. 3.C - Prob. 73ECh. 3.C - Prob. 74ECh. 3.C - 75. Propagation of Error. Suppose you want to cut...Ch. 3.C - Prob. 76ECh. 3.C - 77. Random and Systematic Errors. Find a recent...Ch. 3.C - Prob. 78ECh. 3.C - Prob. 79ECh. 3.C - Prob. 80ECh. 3.D - Prob. 1QQCh. 3.D - Prob. 2QQCh. 3.D - Prob. 3QQCh. 3.D - Prob. 4QQCh. 3.D - Prob. 5QQCh. 3.D - Prob. 6QQCh. 3.D - 7. Over the past three decades, the cost of...Ch. 3.D - Suppose your salary has been rising at a greater...Ch. 3.D - Prob. 9QQCh. 3.D - Prob. 10QQCh. 3.D - Prob. 1ECh. 3.D - What is the Consumer Price Index (CPI)? How is it...Ch. 3.D - Prob. 3ECh. 3.D - Prob. 4ECh. 3.D - Prob. 5ECh. 3.D - Even though my salary has remained the same for...Ch. 3.D - Benjamin Franklin said, “A penny saved is a penny...Ch. 3.D - The prices of cars have risen steadily, but when...Ch. 3.D - 9. When we chart today’s price of milk in 1995...Ch. 3.D - 10. The Consumer Price Index is a theoretical...Ch. 3.D - Prob. 11ECh. 3.D - Prob. 12ECh. 3.D - Prob. 13ECh. 3.D - Prob. 14ECh. 3.D - Gasoline Price Index. Use Table 3.2 to answer the...Ch. 3.D - Gasoline Price Index. Use Table 3.2 to answer the...Ch. 3.D - Prob. 17ECh. 3.D - Prob. 18ECh. 3.D - Prob. 19ECh. 3.D - Prob. 20ECh. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Prob. 22ECh. 3.D - Prob. 23ECh. 3.D - 17-26: Understanding the CPI. Use Table 3.4 to...Ch. 3.D - 17-26: Understanding the CPI. Use Table 3.4 to...Ch. 3.D - Understanding the CPI. Use Table 3.4 to answer the...Ch. 3.D - Prob. 27ECh. 3.D - Prob. 28ECh. 3.D - Prob. 29ECh. 3.D - Prob. 30ECh. 3.D - Health Care Spending. Total spending on health...Ch. 3.D - Prob. 32ECh. 3.D - Prob. 33ECh. 3.D - Prob. 34ECh. 3.D - Prob. 35ECh. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Prob. 37ECh. 3.D - Prob. 38ECh. 3.D - Federal Minimum Wage. Use the following table,...Ch. 3.D - Prob. 40ECh. 3.D - Prob. 41ECh. 3.D - Prob. 42ECh. 3.D - Fan Cost Index. The cost of attending a major...Ch. 3.D - Prob. 44ECh. 3.D - Consumer Price Index. Find a recent news report...Ch. 3.D - Prob. 46ECh. 3.D - Consumer Confidence Index. Use a search engine to...Ch. 3.D - Prob. 48ECh. 3.D - Prob. 49ECh. 3.D - Prob. 50ECh. 3.D - Prob. 51ECh. 3.D - Prob. 52ECh. 3.D - Prob. 53ECh. 3.D - Prob. 54ECh. 3.D - Prob. 55ECh. 3.E - Study Table 3.5. What does the number “8” in the...Ch. 3.E - Study Table 3.5. Which statement is not supported...Ch. 3.E - During their freshman year, Derek’s GPA was 3.4...Ch. 3.E - A false negative in a cancer screening test means...Ch. 3.E - A false positive in a test for steroids means that...Ch. 3.E - Study Table 3.7. The total number of women who did...Ch. 3.E - Study Table 3.7. The total number of women whose...Ch. 3.E - Suppose that a home pregnancy test is 99%...Ch. 3.E - Study the graph in Figure 3.5a. Which of the...Ch. 3.E - Study the graph in Figure 3.5b. Which of the...Ch. 3.E - Prob. 1ECh. 3.E - Prob. 2ECh. 3.E - Prob. 3ECh. 3.E - Prob. 4ECh. 3.E - Despite the fact that the new drug lowered blood...Ch. 3.E - Prob. 6ECh. 3.E - Baggage screening machines are 98% accurate in...Ch. 3.E - The polygraph test showed that the suspect was...Ch. 3.E - The Republications claim the tax cut benefits...Ch. 3.E - The agency suffered a real cut in its annual...Ch. 3.E - Prob. 11ECh. 3.E - Prob. 12ECh. 3.E - Prob. 13ECh. 3.E - Prob. 14ECh. 3.E - Prob. 15ECh. 3.E - Prob. 16ECh. 3.E - Prob. 17ECh. 3.E - Prob. 18ECh. 3.E - Prob. 19ECh. 3.E - Political Math. Government spending for a popular...Ch. 3.E - Basketball Records. Consider the following...Ch. 3.E - 22. Better Drug. Two drugs, A and B, were tested...Ch. 3.E - Prob. 23ECh. 3.E - Airline Arrivals. The following table shows real...Ch. 3.E - Prob. 25ECh. 3.E - Prob. 26ECh. 3.E - Analyzing a Two-Way Table. In the Senate of the...Ch. 3.E - Prob. 28ECh. 3.E - 29. A Tax Cut. According to an analysis of a...Ch. 3.E - Prob. 30ECh. 3.E - Drug Testing. Explore the issue of drug testing...Ch. 3.E - Prob. 32ECh. 3.E - Prob. 33E
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