Several decades ago a large proportion of Americans smoked cigarettes. However, in recent years many adults have quit. To measure the extent of current smoking a random sample of American adults was asked to report whether they smoked (1 = yes, 2 = no). There are 244,137,873 American adults. Estimate with 95% confidence the number of American adults who smoke cigarettes.
> The amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events. a. The student requires more than 55 minutes to c
> Most televised baseball games display a pitch tracker that shows whether the pitch was in the strike zone, which in turn shows whether the umpire made the correct call. Major League Baseball keeps track of how well each umpire calls games. Batters swing
> In a Gallup survey, Americans were asked about their main source of news about current events around the world. If 20% of the population report that their main source is television news, find the probability that in a sample of 500 at least 22% say that
> In 2014, approximately 13% of nonelderly Americans adults had no health insurance. Suppose that a random sample of 400 such individuals was drawn. What is the probability that 15% or more had no health insurance?
> Refer to Exercise 9.55. A survey of a random sample of 1,200 undergraduate business students indicates that 336 students plan to major in accounting. What does this tell you about the professor’s claim? Data from Exercise 9.55: An accounting professor c
> An accounting professor claims that no more than one-quarter of undergraduate business students will major in accounting. What is the probability that in a random sample of 1,200 undergraduate business students, 336 or more will major in accounting?
> The Red Lobster restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer testing service wants to examine the claim by asking 460
> A psychologist believes that 80% of male drivers when lost continue to drive hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 350 male drivers and asked each what they did when lost. If
> A university bookstore claims that 50% of its customers are satisfied with the service and prices. a. If this claim is true, what is the probability that in a random sample of 600 customers less than 45% are satisfied? b. Suppose that in a random sample
> The Laurier Company’s brand has a market share of 30%. Suppose that 1,000 consumers of the product are asked in a survey which brand they prefer. What is the probability that more than 32% of the respondents say they prefer the Laurier brand?
> A commercial for a manufacturer of household appliances claims that 3% of all its products require a service call in the first year. A consumer protection association wants to check the claim by surveying 400 households that recently purchased one of the
> A uniformly distributed random variable has minimum and maximum values of 20 and 60, respectively. a. Draw the density function. b. Determine P(35 < X < 45). c. Draw the density function including the calculation of the probability in part (b).
> The manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 14%. What is the probability that in the next 100 customers at least 10% will be tea drinkers?
> a. The manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just two aspirins is 53%. What is the probability that in a random sample of 400 headache sufferers, less than 50% obtain relief? If 50% of the sample act
> The assembly line that produces an electronic component of a missile system has historically resulted in a 2% defective rate. A random sample of 800 components is drawn. What is the probability that the defective rate is greater than 4%? Suppose that in
> The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 55%. What is the probability that in a random sample of 500 voters less than 49% say they will vote for the incumbent?
> A binomial experiment where p = .4 is conducted. Find the probability that in a sample of 60 the proportion of successes exceeds .35.
> Determine the probability that in a sample of 100 the sample proportion is less than .75 if p = .80.
> a. The probability of success on any trial of a binomial experiment is 25%. Find the probability that the proportion of successes in a sample of 500 is less than 22%. b. Repeat part (a) with n = 800. c. Repeat part (a) with n = 1,000.
> a. In a binomial experiment with n = 300 and p = .5, find the probability that P^ is greater than 60%. b. Repeat part (a) with p = .55. c. Repeat part (a) with p = .6
> Xis normally distributed with mean 50 and standard deviation 8. What value of X is such that only 8% of values are below it?
> The property tax paid by homeowners in a large city was determined to be normally distributed with a mean of $2,800 and a standard deviation of $400. A random sample of four homes was drawn. a. What is the probability distribution of the mean of the samp
> A random variable is uniformly distributed between 100 and 150. a. Draw the density function. b. Find P(X > 110). c. Find P(120 < X < 135). d. Find P(X < 122).
> The number of pages produced by a fax machine in a busy office is normally distributed with a mean of 275 and a standard deviation of 75. Determine the probability that in 1 week (5 days) more than 1,500 faxes will be received?
> The restaurant in a large commercial building provides coffee for the occupants in the building. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new t
> Refer to Exercise 9.36. Does your answer change if you discover that the times needed to mark a midterm test are not normally distributed? Data from Exercise 9.36: The time it takes for a statistics professor to mark his midterm test is normally distrib
> The time it takes for a statistics professor to mark his midterm test is normally distributed with a mean of 4.8 minutes and a standard deviation of 1.3 minutes. There are 60 students in the professor’s class. What is the probability that he needs more t
> Refer to Exercise 9.34. Suppose that the professor discovers that the weights of people who use the elevator are normally distributed with an average of 75 kilograms and a standard deviation of 10 kilograms. Calculate the probability that the professor s
> The sign on the elevator in an office tower states, “Maximum Capacity 1,140 kilograms (2,500 pounds) or 16 Persons.” A professor of statistics wonders what the probability is that 16 persons would weigh more than 1,140 kilograms. Discuss what the profess
> The number of customers who enter a supermarket each hour is normally distributed with a mean of 600 and a standard deviation of 200. The supermarket is open 16 hours per day. What is the probability that the total number of customers who enter the super
> The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. Suppose that you draw a random sam
> The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours. a. What is the probability that a randomly selected North American adult watches televisio
> The marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6. a. What proportion of the class has a midterm mark of less than 75? b. What is the probability that a class of 50 has an average midterm mark
> Refer to Example 3.3. From the histogram of the marks, estimate the following probabilities. a. P(55 b. P(X > 65) c. P(X d. P(75 Data from Example 3.3: 30 25 20 15 10 Б 50 60 70 80 90 100 Marks LO Asuenbey
> The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3. a. What proportion of students consume more than 12 pizzas per month? b. What is the probability that in a random samp
> The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. a. What is the probability that a professor works for more than 60 hours per week? b. Find the
> Refer to Exercise 9.26. Does your answer change if you discover that mortgages are not normally distributed? Data from Exercise 9.26: Statisticians determined that the mortgages of homeowners in a city is normally distributed with a mean of $250,000 and
> Statisticians determined that the mortgages of homeowners in a city is normally distributed with a mean of $250,000 and a standard deviation of $50,000. A random sample of 100 homeowners was drawn. What is the probability that the mean is greater than $2
> An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean = 117 cm and standard deviation = 5.2 cm. a. Find the probability that one selected subcomponent is longe
> Refer to Exercise 9.23. If the population of women’s heights is not normally distributed, which, if any, of the questions can you answer? Explain. Data from Exercise 9.23: The heights of North American women are normally distributed with a mean of 64 in
> The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. a. What is the probability that a randomly selected woman is taller than 66 inches? b. A random sample of four women is selected.
> a. Suppose that the standard deviation of a population with N = 10,000 members is 500. Determine the standard error of the sampling distribution of the mean when the sample size is 1,000. b. Repeat part (a) when n = 500. c. Repeat part (a) when n = 100.
> a. Calculate the finite population correction factor when the population size is N = 1,000 and the sample size is n = 100. b. Repeat part (a) when N = 3,000. c. Repeat part (a) when N = 5,000. d. What have you learned about the finite population correcti
> Repeat Exercise 9.18 for a standard deviation of 20. Data from Exercise 9.18: Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample of a. 4 has a mean between 49 and 52. b. 16 has a mean
> Refer to Example 3.2. Estimate the following from the histogram of the returns on investment B. a. P(X > 45) b. P(10 c. P(X d. P(35 Data from Example 3.2: Histogram of Returns on Investment B 18 16 14 12 10 -30 -15 0 15 30 45 60 75 Returns Aauen
> Repeat Exercise 9.18 for a standard deviation of 10. Data from Exercise 9.18: Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample of a. 4 has a mean between 49 and 52. b. 16 has a mean
> Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample of a. 4 has a mean between 49 and 52. b. 16 has a mean between 49 and 52. c. 25 has a mean between 49 and 52.
> Repeat Exercise 9.15 with n = 100. Data from Exercise 9.15: A sample of n = 16 observations is drawn from a normal population with μ = 1,000 and σ = 200. Find the following. a. P(X > 1,050) b. P(X < 960) c. P(X > 1,100)
> Unfortunately, robbery is an all-too frequent crime. Bank robberies tend to be the most lucrative for criminals. In most cases banks do not report the size of the loss. However, several researchers were able to gain access to bank robberies in England. H
> Wages and salaries make up only part of a total compensation. Other parts include paid leave, health insurance, and many others. In 2013, wages and salaries among manufacturers in the United States made up an average of 65.8% of total compensation. To de
> In 2015, there were 124,587,000 (Source: United States Census) households in the United States. There were 81,716,000 family households made up of married couples, single male, and single female households. To determine how many of each type a survey was
> Refer to Exercise 12.165. In 2006 the financial obligations ratio for renters was 23.65. Can we infer that financial obligations ratio for renters has increased between 2016 and this year? Data from Exercise 12.165: Another measure of indebtedness is th
> Refer to Exercise 12.164. Another measure of indebtedness is the financial obligations ratio, which adds automobile lease payments, rental on tenant occupied property, homeowner’s insurance, and property tax payments to the debt service ratio. In 2016, t
> In 2016, the average household debt service ratio for homeowners was 10.02. The household debt service ratio is the ratio of debt payments to disposable personal income. Debt payments consist of mortgage payments and payments on consumer debts. To determ
> Unfortunately, it is not uncommon for high school students in the United States to carry weapons (guns, knives, or clubs). To determine how prevalent this practice is, a survey of high school students was undertaken. Students were asked whether they carr
> Jim Cramer hosts CNBC’s “Mad Money” program. Mr. Cramer regularly makes suggestions about which stocks to buy and sell. How well has Mr. Cramer’s picks performed over the past two years (2005 to 2007)? To answer the question a random sample of Mr. Cramer
> The owner of a downtown parking lot suspects that the person he hired to run the lot is stealing some money. The receipts as provided by the employee indicate that the average number of cars parked in the lot is 125 per day and that, on average, each car
> Exercise 12.159, suppose that the promoter decided to draw a sample of size 600 (because of financial considerations). Each teenager was asked whether he or she would attend the concert (2 = Yes, I will attend; 1 = No, I will not attend). Estimate with 9
> A rock promoter is in the process of deciding whether to book a new band for a rock concert. He knows that this band appeals almost exclusively to teenagers. According to the latest census, there are 400,000 teenagers in the area. The promoter decides to
> An oil company sends out monthly statements to its customers who purchased gasoline and other items using the company’s credit card. Until now, the company has not included a preaddressed envelope for returning payments. The average and the standard devi
> An advertisement for a major home appliance manufacturer claims that its repair personnel are the loneliest in the world because its appliances require the smallest number of service calls. To examine this claim, a researcher drew a random sample of 100
> Refer to Exercise 12.155. Suppose the engineers recoded the data so that springs that were the correct length were recorded as 1, springs that were too long were recorded as 2, and springs that were too short were recorded as 3. Can we infer at the 10% s
> Engineers who are in charge of the production of springs used to make car seats are concerned about the variability in the length of the springs. The springs are designed to be 500 mm long. When the springs are too long, they will loosen and fall out. Wh
> Obesity is defined as having a Body Mass Index (BMI = 30 grams/kilogram2) over 30. A statistics practitioner took a random sample of American adults and classified their BMI as either 1. Under 20, 2. 20–30, 3. Over 30. There are 234,564,000 American adul
> The manager of a branch of a major bank wants to improve service. She is thinking about giving $1 to any customer who waits in line for a period of time that is considered excessive. (The bank ultimately decided that more than 8 minutes is excessive.) Ho
> A national health care system was an issue in recent presidential election campaign and is likely to be a subject of debate for many years. The issue arose because of the large number of Americans who have no health insurance. Under the present system, f
> The routes of postal deliverers are carefully planned so that each deliverer works between 7 and 7.5 hours per shift. The planned routes assume an average walking speed of 2 miles per hour and no shortcuts across lawns. In an experiment to examine the am
> Refer to Exercise 12.148. Also recorded was the amount of time to commute to work on an average day. Estimate with 90% confidence the average commute time. Data from Exercise 12.148: There are 138,592,000 workers in the United States. An economist took
> Refer to Exercise 12.148. Estimate with 95% confidence the number of workers who carpooled to work. Data from Exercise 12.148: There are 138,592,000 workers in the United States. An economist took a random sample of 550 workers and recorded how they com
> There are 138,592,000 workers in the United States. An economist took a random sample of 550 workers and recorded how they commuted to work (1 = drive alone, 2 = car pool, 3 = public transportation, 4 = walked, 5 = other, and 6 = worked at home). Is ther
> A random sample of complaints about American airlines was drawn and the type of complaint was recorded (1 = Flight problems (cancellations, delays, etc.), 2 = Customer service (unhelpful employees, inadequate means, or cabin service, treatment of delayed
> In a large state university (with numerous campuses), the marks in an introductory statistics course are normally distributed with a mean of 68%. To determine the effect of requiring students to pass a calculus test (which at present is not a prerequisit
> Opinion Research International surveyed people whose household incomes exceed $50,000 and asked each for their top money-related new year’s resolutions. The responses are: 1. Get out of credit card debt 2. Retire before age 65 3. Die broke 4. Make do wit
> Refer to Exercise 12.143. A sample of 425 pickup trucks and SUVs was drawn and the age of the vehicles was recorded. Estimate with 95% confidence the mean age of trucks and SUVs. Data from Exercise 12.143: An important factor in attempting to predict the
> An important factor in attempting to predict the demand for new cars is the age of the cars already on the road. A random sample of 650 cars was drawn and the age of each car was recorded. Estimate with 99% confidence the age means age of all-American ca
> Refer to Exercise 12.151. Also recorded was the weapon used (1 = firearm, 2 = knife or other cutting instrument, 3 = other, 4 = no weapon). Estimate with 90% confidence the number of crimes where a firearm was not used. Data from Exercise 12.151: The ro
> According to FBI statistics, there were 354,520 robberies in the United States in 2012 (latest statistics available). A random sample of robberies was drawn and the amount of loss was recorded. Estimate with 95% confidence the total loss of all the robbe
> Robots are being used with increasing frequency on production lines to perform monotonous tasks. To determine whether a robot welder should replace human welders in producing automobiles, an experiment was performed. The time for the robot to complete a
> There are 604,474 bridges in the United States. A structural engineering team randomly SAMPLED 850 bridges and categorized each as either structurally deficient (restricted to light vehicles, require immediate rehabilitation to remain open, or are closed
> One of the issues that came up in a recent municipal election was the high cost of housing. A candidate seeking to unseat an incumbent claimed that the average family spends more than 30% of its annual income on housing. A housing expert was asked to inv
> Hazardous materials are constantly being around the country. To help determine how dangerous these events are a statistics practitioner recorded the distances of a random sample of trucks, trains, airplanes, and boats carrying explosives. Estimate with 9
> The National Hockey League’s Florida Panthers play in the BB&T center. The cost of parking is $20. However, Lexus occasionally pays the cost by offering free parking to drivers of Lexus cars. A statistician wanted to estimate the cost of this program. He
> Suppose the survey in the previous exercise also asked those who were not in the top 1% whether they believed that within 5 years they would be in the top 1% (1 = will not be in top 1% within 5 years and 2 = will be in top 1% within 5 years). Estimate wi
> An advertising company was awarded the contract to design advertising for Rolls Royce automobiles. An executive in the firm decided to pitch the product not only to the affluent in the United States but also to those who think they are in the top 1% of i
> Xis normally distributed with mean 100 and standard deviation 20. What is the probability that X is greater than 145?
> The JC Penney department store chain segments the market for women’s apparel by its identification of values. The three segments are: 1. Conservative 2. Traditional 3. Contemporary Questionnaires about personal and family values are used to identify whic
> A California university is investigating expanding its evening programs. It wants to target people between 25 and 55 years old who have completed high school but did not complete college or university. To help determine the extent and type of offerings,
> A new credit card company is investigating various market segments to determine whether it is profitable to direct its advertising specifically at each one. One of the market segments is composed of Hispanic people. According to the United States census,
> Find the probability. P(Z > 4.0)
> Find the probability. P(Z > 0)
> Find the probability. P(Z > 3.09)
> P(−0.71 < Z < −0.33)
> Find the probability. P(1.04 < Z < 2.03)
> Find the probability. P(Z < 2.57)
> Find the probability. P(Z > 1.87)
> Find the probability. P(Z < 2.23)
> Find the probability. P(Z > −1.24)
> Find the probabilities. P(−1.30 < Z < .70)
> Find the probability. P(Z < −2.16)
> Find the probabilities. P(Z < −1.80)
