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7th Edition

Stefan Waner + 1 other

Publisher: Cengage Learning

ISBN: 9781337274203

Chapter 9, Problem 26RE

Textbook Problem

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A random variable *X* has a symmetric distribution and an expected value
*X* is guaranteed to exceed with a probability of at most 10%.

To determine

**To calculate:** The value that *X* is guaranteed to exceed with a probability of at most *X* with symmetric distribution is

**Given Information:**

The expected value of random variable *X* with symmetric distribution is

**Formula Used:**

The mean of the set of values

According to the Chebyshev’s rule, the interval *k* standard deviations of the mean.

**Calculation:**

Consider the expected value of random variable *X* is

Since *X* lie within *k* standard deviations of the mean according to the Chebyshev’s rule and the probability is at least

Since the distribution is symmetric, the value will exceed

Finite Mathematics and Applied Calculus (MindTap Course List)

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Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...Ch. 9.1 - In Exercises 110, classify the random variable X...

Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - In Exercises 1118, (a) say what an appropriate...Ch. 9.1 - The random variable X has this probability...Ch. 9.1 - The random variable X has the probability...Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - In Exercises 2128, give the probability...Ch. 9.1 - 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Highway Safety Exercises 4150 are based on the...Ch. 9.1 - Highway Safety Exercises 4150 are based on the...Ch. 9.1 - Highway Safety Exercises 4150 are based on the...Ch. 9.1 - Highway Safety Exercises 4150 are based on the...Ch. 9.1 - Highway Safety Exercises 4150 are based on the...Ch. 9.1 - Exercises 51 and 52 assume familiarity with...Ch. 9.1 - Exercises 51 and 52 assume familiarity with...Ch. 9.1 - Testing Your Calculator Use your calculator or...Ch. 9.1 - Testing Your Dice Repeat Exercise 53, but this...Ch. 9.1 - Are all infinite random variables necessarily...Ch. 9.1 - Are all continuous random variables necessarily...Ch. 9.1 - If you are unable to compute the (theoretical)...Ch. 9.1 - What do you expect to happen to the probabilities...Ch. 9.1 - Give an example of a real-life situation that can...Ch. 9.1 - Give an example of a real-life situation that can...Ch. 9.1 - How wide should the bars in a histogram be so that...Ch. 9.1 - How wide should the bars in a histogram be so that...Ch. 9.1 - Give at least one scenario in which you might...Ch. 9.1 - Give at least one scenario in which you might...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 110, you are performing five...Ch. 9.2 - In Exercises 1118, X is a binomial variable with...Ch. 9.2 - In Exercises 1118, X is a binomial variable with...Ch. 9.2 - In Exercises 1118, X is a binomial variable with...Ch. 9.2 - In Exercises 1118, X is a binomial variable with...Ch. 9.2 - In Exercises 1118, X is a binomial variable with...Ch. 9.2 - In Exercises 1118, X is a binomial variable with...Ch. 9.2 - In Exercises 1118, X is a binomial variable with...Ch. 9.2 - In Exercises 1118, X is a binomial variable with...Ch. 9.2 - In Exercises 19 and 20, graph the histogram of the...Ch. 9.2 - In Exercises 19 and 20, graph the histogram of the...Ch. 9.2 - In Exercises 21 and 22, graph the histogram of the...Ch. 9.2 - In Exercises 21 and 22, graph the histogram of the...Ch. 9.2 - Internet Addiction The probability that a randomly...Ch. 9.2 - Alien Retirement The probability that a randomly...Ch. 9.2 - 1990s Internet Stock Boom According to a July 1999...Ch. 9.2 - 1990s Internet Stock Boom According to the article...Ch. 9.2 - Job Training (from the GRE Exam in Economics) In a...Ch. 9.2 - Job Training (based on a question from the GRE...Ch. 9.2 - Manufacturing Your manufacturing plant produces...Ch. 9.2 - Manufacturing Compute the probability distribution...Ch. 9.2 - Teenage Pastimes According to a study,15 the...Ch. 9.2 - Other Teenage Pastimes According to the study...Ch. 9.2 - Subprime Mortgages during the Housing Bubble In...Ch. 9.2 - Subprime Mortgages during the Housing Bubble In...Ch. 9.2 - Triple Redundancy To ensure reliable performance...Ch. 9.2 - IQ Scores Mensa is a club for people who have high...Ch. 9.2 - Standardized Tests Assume that on a standardized...Ch. 9.2 - Standardized Tests Assume that on a standardized...Ch. 9.2 - Product Testing It is known that 43% of all the...Ch. 9.2 - Product Testing It is known that 65% of all the...Ch. 9.2 - Quality Control A manufacturer of light bulbs...Ch. 9.2 - Quality Control A manufacturer of light bulbs...Ch. 9.2 - Highway Safety According to a study,18 a male...Ch. 9.2 - Highway Safety: According to the study cited in...Ch. 9.2 - Mad Cow Disease In March 2004 the U.S. Department...Ch. 9.2 - Mad Cow Disease According to the article cited in...Ch. 9.2 - A soccer player is more likely to score on his...Ch. 9.2 - A soccer player takes repeated shots on goal. 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Roulette A roulette wheel has the numbers 1...Ch. 9.3 - Roulette A roulette wheel has the numbers 1...Ch. 9.3 - Teenage Pastimes According to a study,34 the...Ch. 9.3 - Other Teenage Pastimes According to the study...Ch. 9.3 - Manufacturing Your manufacturing plant produces...Ch. 9.3 - Spiders Your pet tarantula, Spider, has a .12...Ch. 9.3 - Exercises 51 and 52 assume familiarity with...Ch. 9.3 - Exercises 51 and 52 assume familiarity with...Ch. 9.3 - Elimination Tournaments In an elimination...Ch. 9.3 - Elimination Tournaments In an elimination...Ch. 9.3 - Elimination Tournaments In an elimination...Ch. 9.3 - Elimination Tournaments In an elimination...Ch. 9.3 - Stock Portfolios You are required to choose...Ch. 9.3 - Risk Management Before making your final decision...Ch. 9.3 - Insurance Schemes The Acme Insurance Company is...Ch. 9.3 - Insurance The Blue Sky Flight Insurance Company...Ch. 9.3 - In a certain set of five scores, there are as many...Ch. 9.3 - In a certain set of scores, the median occurs more...Ch. 9.3 - Your friend Charlesworth claims that the median of...Ch. 9.3 - Your other friend Imogen asserts that Charlesworth...Ch. 9.3 - Must the expected number of times you hit a...Ch. 9.3 - Your statistics instructor tells you that the...Ch. 9.3 - Your grade in a recent midterm was 80%, but the...Ch. 9.3 - Your grade in a recent midterm was 80%, but the...Ch. 9.3 - Slim tells you that the population mean is just...Ch. 9.3 - Explain how you can use a sample to estimate an...Ch. 9.3 - Following is an excerpt from a full-page ad by...Ch. 9.3 - Following is an excerpt from a five-page ad by...Ch. 9.3 - Sonia has just told you that the expected...Ch. 9.3 - If X is a random variable, what is the difference...Ch. 9.4 - In Exercises 18, compute the (sample) variance and...Ch. 9.4 - In Exercises 18, compute the (sample) variance and...Ch. 9.4 - In Exercises 18, compute the (sample) variance and...Ch. 9.4 - In Exercises 18, compute the (sample) variance and...Ch. 9.4 - In Exercises 18, compute the (sample) variance and...Ch. 9.4 - In Exercises 18, compute the (sample) variance and...Ch. 9.4 - In Exercises 18, compute the (sample) variance and...Ch. 9.4 - In Exercises 18, compute the (sample) variance and...Ch. 9.4 - In Exercises 914, calculate the standard deviation...Ch. 9.4 - In Exercises 914, calculate the standard deviation...Ch. 9.4 - In Exercises 914, calculate the standard deviation...Ch. 9.4 - In Exercises 914, calculate the standard deviation...Ch. 9.4 - In Exercises 914, calculate the standard deviation...Ch. 9.4 - In Exercises 914, calculate the standard deviation...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - In Exercises 1524, calculate the expected value,...Ch. 9.4 - 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Commerce You have been told that the average life...Ch. 9.4 - Batmobiles The average life span of a Batmobile is...Ch. 9.4 - Spiderman Coupes The average life span of a...Ch. 9.4 - Teenage Pastimes According to a study,51 the...Ch. 9.4 - Other Teenage Pastimes According to the study...Ch. 9.4 - Teenage Marketing In 2000, 22% of all teenagers in...Ch. 9.4 - Teenage Marketing In 2000, 18% of all teenagers in...Ch. 9.4 - Supermarkets A survey of supermarkets in the...Ch. 9.4 - Video Arcades Your company, Sonic Video, Inc., has...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Distribution of Wealth If we model after-tax...Ch. 9.4 - Aging Exercises 6168 are based on the following...Ch. 9.4 - Aging Exercises 6168 are based on the following...Ch. 9.4 - Aging Exercises 6168 are based on the following...Ch. 9.4 - Aging Exercises 6168 are based on the following...Ch. 9.4 - Aging Exercises 6168 are based on the following...Ch. 9.4 - Aging Exercises 6168 are based on the following...Ch. 9.4 - Aging Exercises 6168 are based on the following...Ch. 9.4 - Aging Exercises 6168 are based on the following...Ch. 9.4 - Electric Grid Stress In early 2000 a Federal...Ch. 9.4 - Electric Grid Stress In early 2000 a Federal...Ch. 9.4 - Electric Grid Stress In early 2000 a Federal...Ch. 9.4 - Electric Grid Stress In early 2000 a Federal...Ch. 9.4 - Which is greater for a given set of data: the...Ch. 9.4 - Suppose you take larger and larger samples of a...Ch. 9.4 - In one Finite Math class, the average grade was...Ch. 9.4 - You are a manager in a precision manufacturing...Ch. 9.4 - If a finite random variable has an expected value...Ch. 9.4 - If the values of X in a population consist of an...Ch. 9.4 - Find an algebraic formula for the population...Ch. 9.4 - Find an algebraic formula for the sample standard...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 18, Z is the standard normal...Ch. 9.5 - In Exercises 914, X has a normal distribution with...Ch. 9.5 - In Exercises 914, X has a normal distribution with...Ch. 9.5 - In Exercises 914, X has a normal distribution with...Ch. 9.5 - In Exercises 914, X has a normal distribution with...Ch. 9.5 - In Exercises 914, X has a normal distribution with...Ch. 9.5 - In Exercises 914, X has a normal distribution with...Ch. 9.5 - Find the probability that a normal variable takes...Ch. 9.5 - Find the probability that a normal variable takes...Ch. 9.5 - Find the probability that a normal variable takes...Ch. 9.5 - Find the probability that a normal variable takes...Ch. 9.5 - Suppose X is a normal random variable with mean...Ch. 9.5 - Suppose X is a normal random variable with mean...Ch. 9.5 - Suppose X is a normal random variable with mean...Ch. 9.5 - Suppose X is a normal random variable with mean...Ch. 9.5 - If you roll a die 100 times, what is the...Ch. 9.5 - If you roll a die 100 times, what is the...Ch. 9.5 - If you roll a die 200 times, what is the...Ch. 9.5 - If you roll a die 200 times, what is the...Ch. 9.5 - SAT Scores SAT test scores are normally...Ch. 9.5 - SAT Scores SAT test scores are normally...Ch. 9.5 - LSAT Scores LSAT test scores are normally...Ch. 9.5 - LSAT Scores LSAT test scores are normally...Ch. 9.5 - IQ Scores IQ scores (as measured by the...Ch. 9.5 - IQ Scores Refer to Exercise 31. What percentage of...Ch. 9.5 - IQ Scores Refer to Exercise 31. Find the...Ch. 9.5 - IQ Scores Refer to Exercise 31. Find the...Ch. 9.5 - SAT Scores SAT test scores are normally...Ch. 9.5 - LSAT Scores LSAT test scores are normally...Ch. 9.5 - Baseball The mean batting average in major league...Ch. 9.5 - Baseball The mean batting average in major league...Ch. 9.5 - Marketing Your pickle company rates its pickles on...Ch. 9.5 - Marketing Your hot sauce company rates its sauce...Ch. 9.5 - Distribution of Income If we model after-tax...Ch. 9.5 - Distribution of Income If we model after-tax...Ch. 9.5 - Distribution of Income If we model after-tax...Ch. 9.5 - Distribution of Income If we model after-tax...Ch. 9.5 - Distribution of Income If we model after-tax...Ch. 9.5 - Distribution of Income If we model after-tax...Ch. 9.5 - Comparing IQ Tests IQ scores as measured by both...Ch. 9.5 - Comparing IQ Tests Referring to Exercise 47, for...Ch. 9.5 - Product Repairs The new copier your business...Ch. 9.5 - Product Repairs The new computer your business...Ch. 9.5 - Software Testing Exercises 5156 are based on the...Ch. 9.5 - Software Testing Exercises 5156 are based on the...Ch. 9.5 - Software Testing Exercises 5156 are based on the...Ch. 9.5 - Software Testing Exercises 5156 are based on the...Ch. 9.5 - Software Testing Exercises 5156 are based on the...Ch. 9.5 - Software Testing Exercises 5156 are based on the...Ch. 9.5 - Internet Access In 2010, 71% of all households in...Ch. 9.5 - Television Ratings According to data from the...Ch. 9.5 - Aviation The probability of a plane crashing on a...Ch. 9.5 - Aviation The probability of a plane crashing on a...Ch. 9.5 - Insurance Your company issues flight insurance....Ch. 9.5 - Insurance Refer back to Exercise 61. What is your...Ch. 9.5 - Polls In a certain political poll, each person...Ch. 9.5 - Polls In a certain political poll, each person...Ch. 9.5 - IQ Scores Mensa is a club for people with high...Ch. 9.5 - SAT Scores Another way to qualify for Mensa (see...Ch. 9.5 - Under what assumptions are the estimates in the...Ch. 9.5 - If X is a continuous random variable, what values...Ch. 9.5 - Which is larger for a continuous random variable:...Ch. 9.5 - Which of the following is greater: P(Xb)orP(aXb)?Ch. 9.5 - A uniform continuous distribution is one with a...Ch. 9.5 - Which would you expect to have the greater...Ch. 9.5 - Which would you expect to have a density curve...Ch. 9.5 - Suppose students must perform two tasks: Task 1...Ch. 9 - In Exercises 16, find the probability distribution...Ch. 9 - In Exercises 16, find the probability distribution...Ch. 9 - In Exercises 16, find the probability distribution...Ch. 9 - In Exercises 16, find the probability distribution...Ch. 9 - In Exercises 16, find the probability distribution...Ch. 9 - In Exercises 16, find the probability distribution...Ch. 9 - Use any method to calculate the sample mean,...Ch. 9 - Use any method to calculate the sample mean,...Ch. 9 - Give an example of a sample of four scores with...Ch. 9 - Give an example of a sample of six scores with...Ch. 9 - Give an example of a population of six scores with...Ch. 9 - Give an example of a sample of five scores with...Ch. 9 - A die is constructed in such a way that rolling a...Ch. 9 - A die is constructed in such a way that rolling a...Ch. 9 - A die is constructed in such a way that rolling a...Ch. 9 - A die is constructed in such a way that rolling a...Ch. 9 - A die is constructed in such a way that rolling a...Ch. 9 - A die is constructed in such a way that rolling a...Ch. 9 - A die is constructed in such a way that rolling a...Ch. 9 - A die is constructed in such a way that rolling a...Ch. 9 - A couple has three children; X= the number of...Ch. 9 - A couple has four children; X= the number of boys....Ch. 9 - A random variable X has the following frequency...Ch. 9 - A random variable X has the following frequency...Ch. 9 - A random variable X has expected value =100 and...Ch. 9 - A random variable X has a symmetric distribution...Ch. 9 - A random variable X has a bell-shaped symmetric...Ch. 9 - A random variable X has a bell-shaped symmetric...Ch. 9 - In Exercises 2934 the mean and standard deviation...Ch. 9 - In Exercises 2934 the mean and standard deviation...Ch. 9 - In Exercises 2934 the mean and standard deviation...Ch. 9 - In Exercises 2934 the mean and standard deviation...Ch. 9 - In Exercises 2934 the mean and standard deviation...Ch. 9 - In Exercises 2934 the mean and standard deviation...Ch. 9 - Marketing As a promotional gimmick,...Ch. 9 - Marketing As a promotional gimmick,...Ch. 9 - Marketing As a promotional gimmick,...Ch. 9 - Marketing As a promotional gimmick,...Ch. 9 - Marketing As a promotional gimmick,...Ch. 9 - Marketing As a promotional gimmick,...Ch. 9 - Online Sales The following table shows the number...Ch. 9 - Pollen Marjory Duffin is planning a joint sales...Ch. 9 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 9 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 9 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 9 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 9 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 9 - Mac vs. Windows On average, 5% of all hits by Mac...Ch. 9 - Online Cosmetics OHaganBooks.com has launched a...Ch. 9 - Online Cosmetics OHaganBooks.com has launched a...Ch. 9 - Online Cosmetics OHaganBooks.com has launched a...Ch. 9 - Online Cosmetics OHaganBooks.com has launched a...Ch. 9 - Intelligence Billy-Sean OHagan, now a senior at...Ch. 9 - Intelligence To join Mensa (not necessarily the...Ch. 9 - Intelligence On the basis of information given in...Ch. 9 - Intelligence Mensa allows the results of various...Ch. 9 - Which of the following lists of data would you...Ch. 9 - Which of the following lists of data would you...Ch. 9 - Which of the following lists of data would you...Ch. 9 - Which of the following lists of data would you...Ch. 9 - Which of the following lists of data would you...Ch. 9 - Which of the following lists of data would you...Ch. 9 - Use technology to determine whether the given...Ch. 9 - Use technology to determine whether the given...

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If f is twice differentiable and x0 is an inflection point for f, then the curvature of f at x0 ...

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Suppose that each of the bases of the triangular prism in Exercise 2 has an area of 3.4 in2 and that each later...

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Finding Second Partial DerivativesIn Exercises 3134, find the four second partial derivatives. Observe that the...

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25211 is a Mersenne prime. Find the perfect number associated with this number. Write your answer using exponen...

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Solve each of the following problems using the proper order of operations. (3)3+33(6)(3)(62)

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Find all real solutions of each equation. 3z+14=2

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