Find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results. Thirty-six percent of likely U.S. voters think that the federal government should get more involved in fighting local crime. You randomly select five likely U.S. voters and ask them whether they think that the federal government should get more involved in fighting local crime. The random variable represents the number of likely U.S. voters who think that the federal government should get more involved in fighting local crime.
> A z-score is 0. Which of these statements must be true? Explain your reasoning. a. The mean is 0. b. The corresponding x-value is 0. c. The corresponding x-value is equal to the mean.
> Find three real-life examples of a continuous variable. Which do you think may be normally distributed? Why?
> In your own words, describe the difference between the value of x in a binomial distribution and in a geometric distribution.
> Find the indicated probability using the Poisson distribution. Find P(5) when µ = 9.8.
> Find the indicated probability using the Poisson distribution. Find P(2) when µ = 1.5.
> Find the indicated probability using the Poisson distribution. Find P(3) when µ = 6.
> Find the indicated probability using the Poisson distribution. Find P(4) when µ = 5.
> Find the indicated probability using the geometric distribution. Find P(8) when p = 0.28.
> Use the fact that the variance of the Poisson distribution is σ2 = µ. The mean number of bankruptcies filed per hour by businesses in the United States in 2016 was about 2.8. a. Find the variance and the standard deviation. Interpret the results. b. Fi
> Find the indicated probabilities and interpret the results. The mean MCAT total score in a recent year is 500. A random sample of 32 MCAT total scores is selected. What is the probability that the mean score for the sample is a. less than 503, b. more
> Use the fact that the variance of the Poisson distribution is σ2 = µ. In a recent year, the mean number of strokes per hole for golfer Steven Bowditch was about 4.1. a. Find the variance and standard deviation. Interpret the results. b. Find the probabi
> Use the fact that the mean of a geometric distribution is µ = 1/p and the variance is σ2 = q/p2. A company assumes that 0.5% of the paychecks for a year were calculated incorrectly. The company has 200 employees and examines the payroll records from one
> Find the indicated probability using the geometric distribution. Find P(2) when p = 1.5.
> Use the fact that the mean of a geometric distribution is µ = 1/p and the variance is σ2 = q/p2. A daily number lottery chooses three balls numbered 0 to 9. The probability of winning the lottery is 1/1000. Let x be the number of times you play the lotte
> Binomial experiments require that any sampling be done with replacement because each trial must be independent of the others. The hypergeometric distribution also has two outcomes: success and failure. The sampling, however, is done without replacement.
> An automobile manufacturer finds that 1 in every 2500 automobiles produced has a specific manufacturing defect. a. Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 6000 cars. b. The Poisson dis
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. The mean number
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. In Akron, Ohio,
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. Sixty-eight perc
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. Sixty-eight perc
> Find the indicated probabilities and interpret the results. The mean ACT composite score in a recent year is 20.8. A random sample of 36 ACT composite scores is selected. What is the probability that the mean score for the sample is a. less than 21.6,
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. Sixty-three perc
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. Fifty-one percen
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. The mean number
> Find the indicated probability using the geometric distribution. Find P(1) when p = 0.45.
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. The mean number
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. A cereal maker p
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. A glass manufact
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. The probability
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. Football player
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. A newspaper find
> Find the indicated probabilities and interpret the results. Refer to Exercise 34. A random sample of six days is selected. Find the probability that the mean surface concentration of carbonyl sulfide for the sample is a. between 5.1 and 15.7 picomoles p
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. The mean number
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. An auto parts se
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. The probability
> In your own words, describe the difference between the value of x in a binomial distribution and in the Poisson distribution.
> Find the indicated probability using the geometric distribution. Find P(3) when p = 0.65.
> Identify the unusual values of x in each histogram in Exercises 3–5.
> The histogram represents a binomial distribution with probability of success p. Match the histogram with the appropriate number of trials n. Explain your reasoning. What happens as the value of n increases and p remains the same? a. n = 4 b. n = 8
> The histogram represents a binomial distribution with probability of success p. Match the histogram with the appropriate number of trials n. Explain your reasoning. What happens as the value of n increases and p remains the same? a. n = 4 b. n = 8
> The histogram represents a binomial distribution with probability of success p. Match the histogram with the appropriate number of trials n. Explain your reasoning. What happens as the value of n increases and p remains the same? a. n = 4 b. n = 8
> The histogram represents a binomial distribution with 5 trials. Match the histogram with the appropriate probability of success p. Explain your reasoning. a. p = 0.25 b. p = 0.50 c. p = 0.75 P(x) 0.40 0.30 - 0.20 0.10 0 1 2 3 4 5
> Find the indicated probabilities and interpret the results. Refer to Exercise 33. A random sample of 2 years is selected. Find the probability that the mean amount of black carbon emissions for the sample is a. less than 12.3 gigagrams per year, b. bet
> The histogram represents a binomial distribution with 5 trials. Match the histogram with the appropriate probability of success p. Explain your reasoning. a. p = 0.25 b. p = 0.50 c. p = 0.75 P(x) 0.40 0.30 0.20 0.10 0 1 2 3 4 5
> An assembly line produces 10,000 automobile parts. Twenty percent of the parts are defective. An inspector randomly selects 10 of the parts. a. Use the Multiplication Rule to find the probability that none of the selected parts are defective. (Note that
> Another proposed theory in genetics gives the corresponding probabilities for the four types of plants described in Exercise 37 as 5/16, 4/16, 1/16, and 6/16. Ten plants are selected. Find the probability that 5 will be tall and colorful, 2 will be tall
> According to a theory in genetics, when tall and colorful plants are crossed with short and colorless plants, four types of plants will result: tall and colorful, tall and colorless, short and colorful, and short and colorless, with corresponding probabi
> Find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results. Ten percent of college graduates think that Judge Judy serves on the Supreme Court. You randomly select five college gradua
> Find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results. Thirty-two percent of U.S. employees who are late for work blame oversleeping. You randomly select six U.S. employees who a
> Find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results. Seventy-nine percent of U.S. adults believe that life on other planets is plausible. You randomly select eight U.S. adults
> Find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results. Fifty percent of adults are offended by how men portray women in rap and hip-hop music. You randomly select four adults and
> Find the mean, variance, and standard deviation of the binomial distribution for the given random variable. Interpret the results. Seventy-one percent of U.S. adults think that political correctness is a problem in America today. You randomly select seve
> Find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution. The test scores for the Law School Admission Test (LSAT) in a recent year are normally distributed, with a mean
> a. construct a binomial distribution, b. graph the binomial distribution using a histogram and describe its shape, and c. identify any values of the random variable x that you would consider unusual. Explain your reasoning. Fifty-seven percent of schoo
> The histogram represents a binomial distribution with 5 trials. Match the histogram with the appropriate probability of success p. Explain your reasoning. a. p = 0.25 b. p = 0.50 c. p = 0.75 P(x) 0.40 0.30 0.20 0.10 0 1 2 3 4 5
> a. construct a binomial distribution, b. graph the binomial distribution using a histogram and describe its shape, and c. identify any values of the random variable x that you would consider unusual. Explain your reasoning. Seventy-seven percent of adu
> a. construct a binomial distribution, b. graph the binomial distribution using a histogram and describe its shape, and c. identify any values of the random variable x that you would consider unusual. Explain your reasoning. Fifty-seven percent of emplo
> a. construct a binomial distribution, b. graph the binomial distribution using a histogram and describe its shape, and c. identify any values of the random variable x that you would consider unusual. Explain your reasoning. Forty-nine percent of workin
> Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. Forty-four percent of U.S. adults say they are more likely to make purchases during a sales tax holiday. You randomly select 15 adults. Find the probability that th
> Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. Four percent of the U.S. workforce test positive for illicit drugs. You randomly select 14 workers. Find the probability that the number of workers who test positiv
> Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. Twenty percent of consumers prefer to purchase groceries online. You randomly select 16 consumers. Find the probability that the number of consumers who prefer to p
> Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. Forty percent of consumers prefer to purchase electronics online. You randomly select 11 consumers. Find the probability that the number of consumers who prefer to
> Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. Eleven percent of U.S. adults eat fast food four to six times per week. You randomly select 12 U.S. adults. Find the probability that the number of U.S. adults who
> Find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution. The per capita electric power consumption level in a recent year in Ecuador is normally distributed, with a mea
> Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. Fifty-six percent of U.S. adults say they intend to get a flu shot. You randomly select 10 U.S. adults. Find the probability that the number of U.S. adults who inte
> Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. Thirty-six percent of U.S. adults favor the use of unmanned drones by police agencies. You randomly select nine U.S. adults. Find the probability that the number of
> In a binomial experiment with n trials, what does the random variable measure?
> Find the indicated probabilities. If convenient, use technology or Table 2 in Appendix B. Thirty-four percent of U.S. adults have very little confidence in newspapers. You randomly select eight U.S. adults. Find the probability that the number of U.S. ad
> Determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. A survey found that 42% of
> Determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. A state lottery official r
> Determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. You draw five cards, one a
> Determine whether the experiment is a binomial experiment. If it is, identify a success, specify the values of n, p, and q, and list the possible values of the random variable x. If it is not a binomial experiment, explain why. A survey found that 36% of
> Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 316, p = 0.82
> Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 124, p = 0.26
> A population and sample size are given. a. Find the mean and standard deviation of the population. b. List all samples (with replacement) of the given size from the population and find the mean of each. c. Find the mean and standard deviation of the s
> Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 84, p = 0.65
> Find the mean, variance, and standard deviation of the binomial distribution with the given values of n and p. n = 50, p = 0.4
> Identify the unusual values of x in each histogram in Exercises 6–8.
> In a binomial experiment, what does it mean to say that each trial is independent of the other trials?
> The distribution of SAT mathematics scores for college-bound male seniors in 2016 has a mean of 524 and a standard deviation of 126. The distribution of SAT mathematics scores for college-bound female seniors in 2016 has a mean of 494 and a standard devi
> The distribution of SAT mathematics scores for college-bound male seniors in 2016 has a mean of 524 and a standard deviation of 126. The distribution of SAT mathematics scores for college-bound female seniors in 2016 has a mean of 494 and a standard devi
> Use this information about linear transformations. For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a and b are constants. If the random variable x has mean µx and standard
> Use this information about linear transformations. For a random variable x, a new random variable y can be created by applying a linear transformation y = a + bx, where a and b are constants. If the random variable x has mean µx and standard
> Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. A high school basketball tea
> Find the expected value E(x) to the player for one play of the game. If x is the gain to a player in a game of chance, then E(x) is usually negative. This value gives the average amount per game the player can expect to lose. In American roulette, the wh
> In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. Out of 2000 randomly selected people, about how many would you expect to have IQ scores less than 90?
> In a game of chance, what is the relationship between a “fair bet” and its expected value? Explain.
> The expected value of an accountant’s profit and loss analysis is 0. Explain what this means.
> The histogram shows the reviewer ratings on a scale from 1 (lowest) to 5 (highest) of a recently published book. Reviewer Ratings P(x) 0.445 045 0.40 035 0.30 025 0.238 0.212 0.20 0.15 0.10 0.086 0.05 0.019 Rating Probability
> The histogram shows the distribution of hurricanes that have hit the U.S. mainland from 1851 through 2015 by Saffir-Simpson category, where 1 is the weakest level and 5 is the strongest level. U.S. Mainland Hurricanes P(x) 0.45 0.411 0.40 0.35 0.30 0
> The number of school-related extracurricular activities per student Activities 1 2 3 4 5 6. Probability 0.059 0.122 0.163 0.178 0.213 0.128 0.084 0.053
> The number of defects per 1000 machine parts inspected Defects 1 3 4 5 Probability 0.263 0.285 0.243 0.154 0.041 0.014
> a. Find the mean, variance, and standard deviation of the probability distribution, and b. Interpret the results. The number of games played in each World Series from 1903 through 2016 Games played 4 6. 7 8 Probability 0.188 0.223 0.214 0.348 0.027
> a. Find the mean, variance, and standard deviation of the probability distribution, and b. Interpret the results. The number of dogs per household in a neighborhood Dogs 1 2 3 4 5 Probability 0.686 0.195 0.077 0.022 0.013 0.007
> Determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. 1 3 4 P(x) 2.
> Determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. 1 2 3 4 P(x) 0.30 0.25 0.25 0.15 0.05
> In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. What percent of the IQ scores are greater than 112?
> An online magazine finds that the mean number of typographical errors per page is five. Find the probability that the number of typographical errors found on any given page is a. exactly five, b. less than five, and c. exactly zero.
> Determine the missing probability for the probability distribution. 1 2 3 4 5 6 P(x) 0.05 0.17 0.23 0.21 0.11 0.08
> Determine the missing probability for the probability distribution. 2 3 4 P(x) 0.06 0.12 0.18 0.30
