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Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340

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BuyFindarrow_forward

Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
Publisher: Cengage Learning
ISBN: 9781337625340
Chapter 8, Problem 9T
Textbook Problem
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The random variable x has a normal distribution with mean 22 and standard deviation 8. Find B so that Pr ( x> B )  = 0 .02 .

To determine

To calculate: The value of B for a normal probability distribution Pr(x>B)=0.02 when the mean and the standard deviation is 22 and 8 respectively.

Explanation of Solution

Given Information:

The mean of the discrete distribution is 22, the standard deviation is 8 and x is normally distributed.

Formula used:

The z score for a normally distribution of x is,

z=xμσ

Where, μ is the mean and σ is the standard deviation.

Calculation:

Consider the normal distribution, Pr(x>B)=0.02.

The mean of the distribution is 22,

μ=22

The standard deviation of the distribution is 8,

σ=8

Since, the normal distribution is symmetric about mean 0.5.

Pr(x>B)=0.5P(zB)=0.50.02=0.48

In the appendix C of the book, the value of z0 is 0.4798 for 2.05 and the value of z0 is 0.4803 for 2.06 as the value 0.48 lies between 0.04798 and 0.4803.

From the interpolation method to find the value of z0 corresponds to 0.48.

0.48030.480.48030.4798=2

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Chapter 8 Solutions

Mathematical Applications for the Management, Life, and Social Sciences
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Ch. 8.1 - 7. A fair die is rolled 12 times. What is the...Ch. 8.1 - 8. When a pair of dice is rolled, a sum of 5...Ch. 8.1 - In Problems 9 and 10, five balls are drawn with...Ch. 8.1 - In Problems 9 and 10, five balls are drawn with...Ch. 8.1 - 11. Suppose a pair of dice is thrown 4 times. What...Ch. 8.1 - 12. If a pair of dice is thrown 4 times, find the...Ch. 8.1 - 13. Suppose the probability that a marksman will...Ch. 8.1 - 14. The probability that a sharpshooter will hit a...Ch. 8.1 - 15. Genetics A family has 4 children. If the...Ch. 8.1 - 16. Testing A multiple-choice test has 10...Ch. 8.1 - 17. Management The manager of a store buys marine...Ch. 8.1 - 18. Quality control A hospital buys blood pressure...Ch. 8.1 - 19. Safety devices A fire detection device uses 4...Ch. 8.1 - 20. Genetics The probability that a certain couple...Ch. 8.1 - 21. Health care Suppose that of the patients who...Ch. 8.1 - 22. Employee benefits In a certain school...Ch. 8.1 - 23. Genetics If the ratio of boys born to girls...Ch. 8.1 - 24. Biology It has been determined empirically...Ch. 8.1 - 25. Insurance If records indicate that 4 houses...Ch. 8.1 - 26. Psychology Suppose 4 rats are placed in a...Ch. 8.1 - 27. Sports A baseball player has a lifetime...Ch. 8.1 - 28. Quality control If the probability of an...Ch. 8.1 - 29. Quality control A company produces shotgun...Ch. 8.1 - 30. Quality control A baseball pitching machine...Ch. 8.1 - 31. Testing A quiz consists of 10 multiple-choice...Ch. 8.1 - 32. Demographics In a certain community, 10% of...Ch. 8.1 - 33. Suicide rates Suppose the probability of...Ch. 8.2 - Consider the data 10, 12, 12, 8, 30, 12, 8, 10, 5,...Ch. 8.2 - Consider the data 10, 12, 12, 8, 30, 12, 8, 10, 5,...Ch. 8.2 - Consider the data 10, 12, 12, 8, 30, 12, 8, 10, 5,...Ch. 8.2 - 4. Find the standard deviation of the data: 10,...Ch. 8.2 - Construct frequency histograms for the data given...Ch. 8.2 - Construct frequency histograms for the data given...Ch. 8.2 - Construct frequency histograms for the data given...Ch. 8.2 - Construct frequency histograms for the data given...Ch. 8.2 - Construct frequency histograms for the data given...Ch. 8.2 - Construct frequency histograms for the data given...Ch. 8.2 - Construct frequency histograms for the data given...Ch. 8.2 - Construct frequency histograms for the data given...Ch. 8.2 - Find the modes of the sets of scores in Problems...Ch. 8.2 - Find the modes of the sets of scores in Problems...Ch. 8.2 - Find the modes of the sets of scores in Problems...Ch. 8.2 - Find the modes of the sets of scores in Problems...Ch. 8.2 - Find the medians of the sets of scores in Problems...Ch. 8.2 - Find the medians of the sets of scores in Problems...Ch. 8.2 - Find the medians of the sets of scores in Problems...Ch. 8.2 - Find the medians of the sets of scores in Problems...Ch. 8.2 - Find the modes, medians, and means of the scores...Ch. 8.2 - Find the modes, medians, and means of the scores...Ch. 8.2 - Find the modes, medians, and means of the scores...Ch. 8.2 - Find the modes, medians, and means of the scores...Ch. 8.2 - Find the modes, medians, and means of the scores...Ch. 8.2 - Find the modes, medians, and means of the scores...Ch. 8.2 - 23. 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Cell phones...Ch. 8.2 - Assume all data are sample data. 40. Product...Ch. 8.2 - Assume all data are sample data. 41. Real estate...Ch. 8.2 - Assume all data are sample data. 42. Birth weights...Ch. 8.2 - Assume all data are sample data. 43. Renewable...Ch. 8.2 - Assume all data are sample data. 44. Malpractice...Ch. 8.2 - Assume all data are sample data. 45. Aged...Ch. 8.2 - Assume all data are sample data. 46. Beet sugar...Ch. 8.2 - Assume all data are sample data. 47. Disposable...Ch. 8.2 - Assume all data are sample data. 48. Salaries S &...Ch. 8.2 - Assume all data are sample data. 49. Salaries...Ch. 8.2 - Assume all data are sample data. 50. Sales A new...Ch. 8.2 - Assume all data are sample data. 51. Insurance...Ch. 8.2 - Assume all data are sample data. 52. Youth...Ch. 8.2 - Assume all data are sample data. 53. Public...Ch. 8.2 - Assume all data are sample data. 54. Private...Ch. 8.3 - 1. Consider a game in which you roll a the and...Ch. 8.3 - 2. 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Test results At a major university, exam...Ch. 8.4 - 44. Budgeting The amount spent monthly, x, for...Ch. 8.4 - 45. Quality control The milk machine at a large...Ch. 8.4 - 46. Manufacturing A textile manufacturer produces...Ch. 8.4 - 47. College standards At a certain college, CPAs...Ch. 8.5 - 1. Which of the following binomial probability...Ch. 8.5 - 2. Suppose a binomial probability experiment has p...Ch. 8.5 - In Problems 1-4, indicate which of the binomial...Ch. 8.5 - In Problems 1-4, indicate which of the binomial...Ch. 8.5 - In Problems 1-4, indicate which of the binomial...Ch. 8.5 - In Problems 1-4, indicate which of the binomial...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - For the binomial experiments in Problems 5-18,...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8.5 - In the following problems, use a normal...Ch. 8 - 1. If the probability of success on each trial of...Ch. 8 - A bag contains 5 black balls and 7 white balls. If...Ch. 8 - 3. If a die is rolled 4 times, what is the...Ch. 8 - Use the data in the frequency table in Problems...Ch. 8 - Use the data in the frequency table in Problems...Ch. 8 - Use the data in the frequency table in Problems...Ch. 8 - Use the data in the frequency table in Problems...Ch. 8 - 8. Construct a frequency histogram for the...Ch. 8 - 9. What is the median of the scores in Problem...Ch. 8 - 10. What is the mean of the scores in Problem 8? Ch. 8 - 11. What is the mean of the scores in Problem 8? Ch. 8 - 12. Find the mean, variance, and standard...Ch. 8 - 13. Find the mean, variance, and standard...Ch. 8 - 14. For the following probability distribution,...Ch. 8 - Determine whether each function or table in...Ch. 8 - Determine whether each function or table in...Ch. 8 - Determine whether each function or table in...Ch. 8 - Determine whether each function or table in...Ch. 8 - 19. For the probability distribution shown, find...Ch. 8 - 20. For the discrete probability distribution...Ch. 8 - 21. For the probability distribution shown, find...Ch. 8 - 22. A coin has been altered so that the...Ch. 8 - 23. Suppose a pair of dice is thrown 18 times. How...Ch. 8 - 24. Expand . Ch. 8 - 25. What is the area under the standard normal...Ch. 8 - 26. If z is a standard normal score, find . Ch. 8 - 27. Find Pr . Ch. 8 - 28. If a variable x is normally distributed, with ...Ch. 8 - 29. If a variable x is normally distributed, with ...Ch. 8 - 30. If a variable x is normally distributed, with ...Ch. 8 - 31. Find the number A so that for the standard...Ch. 8 - For the binomial distributions in Problems 32 and...Ch. 8 - For the binomial distributions in Problems 32 and...Ch. 8 - For the binomial experiments in Problems 34-37,...Ch. 8 - For the binomial experiments in Problems 34-37,...Ch. 8 - For the binomial experiments in Problems 34-37,...Ch. 8 - For the binomial experiments in Problems 34-37,...Ch. 8 - 38. Genetics Suppose the probability that a...Ch. 8 - 39. Sampling Suppose of a population opposes a...Ch. 8 - 40. Crime Suppose of the population are victims...Ch. 8 - 41. Disease One person in 100,000 develops a...Ch. 8 - Farm families The distribution of farm families...Ch. 8 - Farm families The distribution of farm families...Ch. 8 - Fanti families The distribution of farm families...Ch. 8 - 45. Cancer testing The probability that a man with...Ch. 8 - 46. Fraud A company selling substandard drugs to...Ch. 8 - 47. Racing Suppose you paid $2 for a bet on a...Ch. 8 - 48. Lotteries A state lottery pays $500 to anyone...Ch. 8 - 49. Crime Refer to Problem 40. (a) What is the...Ch. 8 - 50. Testing Suppose the mean SAT score for...Ch. 8 - 51. Net worth Suppose the mean net worth of the...Ch. 8 - 52. Testing The length of time it takes to...Ch. 8 - In Problems 53-56, use a normal approximation. 53....Ch. 8 - In Problems 53-56, use a normal approximation. 54....Ch. 8 - In Problems 53-56, use a normal approximation. 55....Ch. 8 - In Problems 53-56, use a normal approximation. 56....Ch. 8 - 1. If a coin is “loaded” so that the probability...Ch. 8 - 2. Suppose the coin in Problem 1 is tossed 12...Ch. 8 - 3. If x is a random variable, what properties must...Ch. 8 - 4. Find the expected value of the variable x for...Ch. 8 - 5. For the probability distribution shown, find...Ch. 8 - 6. For the sample data in the table, find the...Ch. 8 - 7. If the variable x is normally distributed, with...Ch. 8 - 8. For the normal distribution with mean 70 and...Ch. 8 - 9. The random variable x has a normal distribution...Ch. 8 - 10. Use a normal approximation to a binomial...Ch. 8 - 11. Use a normal approximation to a binomial...Ch. 8 - The table gives the ages of a sample of...Ch. 8 - The table gives the ages of a sample of...Ch. 8 - 14. The table gives the projected 2020 population...Ch. 8 - 15. The table summarizes the number of mobile...Ch. 8 - 16. Suppose that 2% of the computer chips shipped...Ch. 8 - The table gives the percent of women who become...Ch. 8 - The table gives the percent of women who become...Ch. 8 - The table gives the percent of women who become...Ch. 8 - 20. A new light bulb has an expected life of...Ch. 8 - 21. Hargray Communications offered a bundled...Ch. 8 - 22. A juice manufacturer sells several kinds of...Ch. 8 - One of the reasons the Powerball Lottery (offered...Ch. 8 - I. Lotteries One of the reasons the Powerball...

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