You are analyzing the sample of bolts in Exercise 13. The population standard deviation of the bolts’ diameters should be less than 0.5 inch. Does the confidence interval you constructed for s suggest that the variation in the bolts’ diameters is at an acceptable level? Explain your reasoning.
> 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
> In Exercise 20, would it be unusual for an employee to work two hours of overtime? Explain your reasoning.
> In Exercise 19, would it be unusual for a household to have no HD televisions? Explain your reasoning.
> Use the probability distribution you made in Exercise 20 to find the probability of randomly selecting an employee whose overtime is a. one or two hours, b. two hours or less, c. between three and six hours, inclusive, d. between one and three hours,
> Use the probability distribution you made in Exercise 19 to find the probability of randomly selecting a household that has a. one or two HD televisions, b. two or more HD televisions, c. between one and three HD televisions, inclusive, and d. at mos
> a. construct a probability distribution, and b. graph the probability distribution using a histogram and describe its shape. The number of overtime hours worked in one week per employee Overtime hours 0 1 2 3 4 5 6 Employees 6 12 29 57 42 30 16
> a. construct a probability distribution, and b. graph the probability distribution using a histogram and describe its shape. The number of high-definition (HD) televisions per household in a small town Televisions 0 1 2 3 Households 26 442 728 1404
> Determine whether the random variable x is discrete or continuous. Explain. Let x represent the snowfall (in inches) in Nome, Alaska, last winter.
> Determine whether the random variable x is discrete or continuous. Explain. Let x represent the number of texts a student sends in one day.
> In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. Find the probability that a randomly selected person has an IQ score between 95 and 105. Is this an unusual event? Explain.
> Determine whether the random variable x is discrete or continuous. Explain. Let x represent the number of tornadoes in the month of May in Oklahoma.
> Determine whether the random variable x is discrete or continuous. Explain. Let x represent the volume of blood drawn for a blood test.
> Determine whether the random variable x is discrete or continuous. Explain. Let x represent the length of time it takes to complete an exam.
> Determine whether the random variable x is discrete or continuous. Explain. Let x represent the number of cars in a university parking lot.
> Determine whether the graph on the number line represents a discrete random variable or a continuous random variable. Explain your reasoning. The total annual arrests (in millions) in the United States 10 11 12 13 Arrests
> Determine whether the graph on the number line represents a discrete random variable or a continuous random variable. Explain your reasoning. The distance a baseball travels 12. The total annual arrests (in millions) after being hit 100 200 300 400 5
> Determine whether the graph on the number line represents a discrete random variable or a continuous random variable. Explain your reasoning. The length of time student-athletes practice each week 8 12 16 20 Time (in hours)
> Determine whether the graph on the number line represents a discrete random variable or a continuous random variable. Explain your reasoning. The attendance at concerts for 10. The length of time student-athletes a rock group 40,000 45,000 50,000 Att
> Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The expected value of a random variable can never be negative.
> Construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Assume the sample is from a normally distributed population. c = 0.95, σ2 = 11.56, n = 30
> In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. Find the probability that a randomly selected person has an IQ score higher than 125. Is this an unusual event? Explain.
> Find the critical values x2R and x2L for the level of confidence c and sample size n. c = 0.80, n = 51
> Find the critical values x2R and x2L for the level of confidence c and sample size n. c = 0.99, n = 30
> Find the critical values x2R and x2L for the level of confidence c and sample size n. c = 0.98, n = 26
> Find the critical values x2R and x2L for the level of confidence c and sample size n. c = 0.95, n = 20
> Find the critical values x2R and x2L for the level of confidence c and sample size n. c = 0.99, n = 15
> Find the critical values x2R and x2L for the level of confidence c and sample size n. c = 0.90, n = 8
> In your own words, explain how finding a confidence interval for a population variance is different from finding a confidence interval for a population mean or proportion.
> You are analyzing the sample of waiting times in Exercise 23. The population standard deviation of the waiting times should be less than 2.5 minutes. Does the confidence interval you constructed for s suggest that the variation in the waiting times is at
> You are analyzing the sample of car batteries in Exercise 21. The population standard deviation of the batteries’ reserve capacities should be less than 0.25 hour. Does the confidence interval you constructed for s suggest that the variation in the batte
> You are analyzing the sample of cough syrup bottles in Exercise 14. The population standard deviation of the volumes of the bottles’ contents should be less than 0.025 fluid ounce. Does the confidence interval you constructed for s suggest that the varia
> The random variable x is normally distributed with the given parameters. Find each probability. a. µ = 9.2, σ ≈ 1.62, P(x < 5.97) b. µ = 87, σ ≈ 19, P(x > 40.5) c. µ = 5.5, σ ≈ 0.08, P(5.36 < x < 5.64) d. µ = 18.5, σ ≈ 4.25, P(19.6 < x < 26.1)
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The prices of a random sample of 20 new m
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The waiting times (in minutes) of a rando
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The record high daily temperatures (in de
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The reserve capacities (in hours) of 18 r
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. As part of a survey, you ask a random sam
> What happens to the shape of the chi-square distribution as the degrees of freedom increase?
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. As part of a water quality survey, you te
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The numbers of touchdowns scored by 11 ra
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The durations (in days) of 14 randomly se
> Find each probability using the standard normal distribution. a. P(z > -1.68) b. P(z < 2.23) c. P(-0.47 < z < 0.47) d. P(z < -1.992 or z > -0.665)
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The final exam scores of 24 randomly sele
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The annual earnings
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The volumes (in flu
> Assume the sample is from a normally distributed population and construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Interpret the results. The diameters (in i
> Construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Assume the sample is from a normally distributed population. c = 0.98, σ = 278.1, n = 41
> Construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Assume the sample is from a normally distributed population. c = 0.90, σ = 35, n = 18
> Construct the indicated confidence intervals for a. the population variance σ2 and b. the population standard deviation σ. Assume the sample is from a normally distributed population. c = 0.99, σ2 = 0.64, n = 7
> Does a population have to be normally distributed in order to use the chi-square distribution?
> Use the confidence interval to find the margin of error and the sample proportion. (0.512, 0.596)
> Use the confidence interval to find the margin of error and the sample proportion. (0.245, 0.475)
> In a survey of U.S. adults, 16% say they have had someone take over their email accounts without their permission. You randomly select 250 U.S. adults and ask them whether they have had someone take over their email accounts without their permission. Fin
> Use the confidence interval to find the margin of error and the sample proportion. (0.905, 0.933)
> Let p be the population proportion for the situation. Find point estimates of p and q. In a survey of 2016 U.S. adults, 665 believe America should stop terrorism at all costs.
> Let p be the population proportion for the situation. Find point estimates of p and q. In a survey of 2016 U.S. adults, 1310 think mainstream media is more interested in making money than in telling the truth.
> Let p be the population proportion for the situation. Find point estimates of p and q. In a survey of 1040 U.S. adults, 478 believe the government should be able to access encrypted communications when investigating crimes.
> The equation for determining the sample size can be obtained by solving the equation for the margin of error for n. Show that this is true and justify each step. n = pgl E E =
> Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 1052 parents of children ages 8–14, 68% say they are willing to get a second or part-time job to pay for their children’s college education, and 42% s
> Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 3539 U.S. adults, 47% believe the economy is getting better. Three weeks prior to this survey, 53% believed the economy was getting better. The survey
> Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 1035 U.S. adults, 37% say the U.S. spends too little on defense. The survey’s margin of error is ±4%.
> In a survey of U.S. adults, 16% say they have had someone take over their email accounts without their permission. You randomly select 250 U.S. adults and ask them whether they have had someone take over their email accounts without their permission. Det
> Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 1000 U.S. adults, 71% think teaching is one of the most important jobs in our country today. The survey’s margin of error is ±3%.
> Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 1503 U.S. adults, 79% say people have the right to nonviolent protest. The survey’s margin of error is ±2.9%.
> Let p be the population proportion for the situation. Find point estimates of p and q. In a survey of 1040 U.S. adults, 62 have had someone impersonate them to try to claim tax refunds.
> Translate the statement into a confidence interval. Approximate the level of confidence. In a survey of 1003 U.S. adults, 70% said being able to speak English is at the core of national identity. The survey’s margin of error is ±3.4%
> Use the figure, which shows the results of a survey in which 2000 U.S. college graduates from the year 2016 were asked questions about employment. In Exercise 27, does it seem possible that any of the population proportions could be equal? Explain.
> Use the figure, which shows the results of a survey in which 2000 U.S. college graduates from the year 2016 were asked questions about employment. Construct a. a 95% confidence interval and b. a 99% confidence interval for the population proportion of
> Use the figure, which shows the results of a survey in which 1003 adults from the United States, 1020Â adults from Canada, 999 adults from France, 1000 adults from Japan, and 1000 adults from Australia were asked whether national identity is s
> Use the figure, which shows the results of a survey in which 1003 adults from the United States, 1020Â adults from Canada, 999 adults from France, 1000 adults from Japan, and 1000 adults from Australia were asked whether national identity is s
> In Exercise 20(b), would a sample size of 600 be acceptable? Explain. From Exercise 20(b): Find the minimum sample size needed, using a prior study that found that 31% of motor vehicle fatalities were caused by alcohol-impaired driving.
> In Exercise 17(b), would a sample size of 200 be acceptable? Explain. From Exercise 17(b): Find the minimum sample size needed, using a prior survey that found that 25% of U.S. adults think Congress is doing a good or excellent job.
> In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. Are you more likely to randomly select one person with an IQ score greater than 105 or are you more likely to randomly select a sampl
> In Exercise 14, does it seem possible that the population proportion could be within 1% of the point estimate? Explain. From Exercise 14: Construct a 99% confidence interval for the population proportion. Interpret the results. In a survey of 600 United
> In Exercise 11, does it seem possible that the population proportion could equal 0.59? Explain. From Exercise 11: Construct 90% and 95% confidence intervals for the population proportion. Interpret the results and compare the widths of the confidence in
> You wish to estimate, with 95% confidence, the population proportion of motor vehicle fatalities that were caused by alcohol-impaired driving. Your estimate must be accurate within 5% of the population proportion. a. No preliminary estimate is available
> You wish to estimate, with 90% confidence, the population proportion of U.S. adults who eat fast food four to six times per week. Your estimate must be accurate within 3% of the population proportion. a. No preliminary estimate is available. Find the mi
> You wish to estimate, with 99% confidence, the population proportion of U.S. adults who support labeling legislation for genetically modified organisms (GMOs). Your estimate must be accurate within 2% of the population proportion. a. No preliminary esti
> You wish to estimate, with 95% confidence, the population proportion of U.S. adults who think Congress is doing a good or excellent job. Your estimate must be accurate within 4% of the population proportion. a. No preliminary estimate is available. Find
> In a survey of 1000 U.S. adults, 490 oppose allowing transgender students to use the bathrooms of the opposite biological sex. Construct a 90% confidence interval for the population proportion of U.S. adults who oppose allowing transgender students to us
> In a survey of 1,626,773 U.S. adults, 49,311 personally identify as lesbian, gay, bisexual, or transgender. Construct a 95% confidence interval for the population proportion of U.S. adults who personally identify as lesbian, gay, bisexual, or transgender
> Construct a 99% confidence interval for the population proportion. Interpret the results. In a survey of 600 United Kingdom teachers, 226 say they would wear a body camera in school.
> In a standardized IQ test, scores are normally distributed, with a mean score of 100 and a standardized deviation of 15. A random sample of 60 people is selected from this population. What is the probability that the mean IQ score of the sample is greate
