The prior probabilities for events A1 and A2 are P(A1) = .40 and P(A2) = .60. It is also known that P(A1 ∩ A2) = 0. Suppose P(B ∣ A1) = .20 and P(B ∣ A2) = .05. a. Are A1 and A2 mutually exclusive? Explain. b. Compute P(A1 ∩ B) and P(A2 ∩ B). c. Compute P(B). d. Apply Bayes’ theorem to compute P(A1 ∣ B) and P(A2 ∣ B).
> A sample of size 100 is selected from a population with / = .40. a. What is the expected value of /? b. What is the standard error of /? c. Show the sampling distribution of /. d. What does the sampling distribution of / show?
> Fortune publishes data on sales, profits, assets, stockholders’ equity, market value, and earnings per share for the 500 largest U.S. industrial corporations every year. Assume that you want to select a simple random sample of 10 corpor
> Assume the population standard deviation is s = 25. Compute the standard error of the mean, sx, for sample sizes of 50, 100, 150, and 200. What can you say about the size of the standard error of the mean as the sample size is increased?
> The Pew American Trends Survey includes a series of questions on attitudes toward automation. The May 2018 results showed that 2977 of 4135 respondents are worried about a future in which robots and computers can do many human jobs, 2770 are worried abou
> According to Wine-Searcher, wine critics generally use a wine-scoring scale to communicate their opinions on the relative quality of wines. Wine scores range from 0 to 100, with a score of 95–100 indicating a great wine, 90â€
> Morningstar publishes ratings data on 1208 company stocks. A sample of 40 of these stocks is contained in the file Morningstar. Use the Morningstar data set to answer the following questions. a. Develop a point estimate of the proportion of the stocks th
> The following crosstabulation shows the average speed of the 25 winners by year of the Daytona 500 automobile race (The World Almanac). a. Calculate the row percentages. b. What is the apparent relationship between average winning speed and year? What
> Tablet PCs: Cost, CPU, and Operating System. Refer to Table 1.6. a. What is the average cost for the tablets? b. Compare the average cost of tablets with a Windows operating system to the average cost of tablets with an Android operating system. c. Wha
> A sample of 5 months of sales data provided the following information: a. Develop a point estimate of the population mean number of units sold per month. b. Develop a point estimate of the population standard deviation.
> A survey question for a sample of 150 individuals yielded 75 Yes responses, 55 No responses, and 20 No Opinions. a. What is the point estimate of the proportion in the population who respond Yes? b. What is the point estimate of the proportion in the pop
> The following data are from a simple random sample. 5 8 10 7 10 14 a. What is the point estimate of the population mean? b. What is the point estimate of the population standard deviation?
> Using Figure 6.6 as a guide, sketch a normal curve for a random variable x that has a mean of m = 100 and a standard deviation of s = 10. Label the horizontal axis with values of 70, 80, 90, 100, 110, 120, and 130.
> The electric-vehicle manufacturing company Tesla estimates that a driver who commutes 50 miles per day in a Model S will require a nightly charge time of around 1 hour and 45 minutes (105 minutes) to recharge the vehicle’s battery (Tesla company website)
> Delta Airlines quotes a flight time of 2 hours, 5 minutes for its flights from Cincinnati to Tampa. Suppose we believe that actual flight times are uniformly distributed between 2 hours and 2 hours, 20 minutes. a. Show the graph of the probability densit
> A person must score in the upper 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what score must a person h
> The random variable x is known to be uniformly distributed between 10 and 20. a. Show the graph of the probability density function. b. Compute P(x < 15). c. Compute P(12 ≤ x ≤ 18). d. Compute E(x). e. Compute Var(x).
> Draw a graph for the standard normal distribution. Label the horizontal axis at values of −3, −2, −1, 0, 1, 2, and 3. Then use the table of probabilities for the standard normal distribution inside the front cover of the text to compute the following pro
> The random variable x is known to be uniformly distributed between 1.0 and 1.5. a. Show the graph of the probability density function. b. Compute P(x = 1.25). c. Compute P(1.0 ≤ x ≤ 1.25). d. Compute P(1.20 < x < 1.5).
> The Daytona 500 is a 500-mile automobile race held annually at the Daytona International Speedway in Daytona Beach, Florida. The following crosstabulation shows the automobile make by average speed of the 25 winners over a 25 year period (The World Alman
> Employee retention is a major concern for many companies. A survey of Americans asked how long they have worked for their current employer (Bureau of Labor Statistics website). Consider the following example of sample data of 2000 college graduates who g
> The following data were collected by counting the number of operating rooms in use at Tampa General Hospital over a 20-day period: On three of the days only one operating room was used, on five of the days two were used, on eight of the days three were u
> Listed below is a series of experiments and associated random variables. In each case, identify the values that the random variable can assume and state whether the random variable is discrete or continuous.
> The Zagat Restaurant Survey provides food, decor, and service ratings for some of the top restaurants across the United States. For 15 restaurants located in Boston, the average price of a dinner, including one drink and tip, was $48.60. You are leaving
> More and more shoppers prefer to do their holiday shopping online from companies such as Amazon. Suppose we have a group of 10 shoppers; 7 prefer to do their holiday shopping online and 3 prefer to do their holiday shopping in stores. A random sample of
> Suppose N = 15 and r = 4. What is the probability of x = 3 for n = 10?
> According to a 2017 survey conducted by the technology market research firm The Radicati Group, U.S. office workers receive an average of 121 emails per day (Entrepreneur magazine website). Assume the number of emails received per hour follows a Poisson
> According to the National Oceanic and Atmospheric Administration (NOAA), the state of Colorado averages 18 tornadoes every June (NOAA website). (Note: There are 30 days in June.) a. Compute the mean number of tornadoes per day. b. Compute the probability
> To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps. a. List the experimental outcomes
> Emergency 911 calls to a small municipality in Idaho come in at the rate of one every 2 minutes. a. What is the expected number of 911 calls in one hour? b. What is the probability of three 911 calls in five minutes? c. What is the probability of no 911
> The following observations are for two quantitative variables, x and y. Develop a crosstabulation for the data, with x as the row variable and y as the column variable. For x use classes of 10–29, 30–49, and so on; f
> Consider a Poisson distribution with m = 3. a. Write the appropriate Poisson probability function. b. Compute f (2). c. Compute f (1). d. Compute P(x ≥ 2).
> According to a 2017 Wired magazine article, 40% of emails that are received are tracked using software that can tell the email sender when, where, and on what type of device the email was opened (Wired magazine website). Suppose we randomly select 50 rec
> A university found that 20% of its students withdraw without completing the introductory statistics course. Assume that 20 students registered for the course. a. Compute the probability that 2 or fewer will withdraw. b. Compute the probability that exact
> The Census Bureau includes nine states in what it defines as the Northeast region of the United States. Assume that the government is interested in tracking unemployment in these nine states and that the random variable of interest is the number of North
> Three students scheduled interviews for summer employment at the Brookwood Institute. In each case the interview results in either an offer for a position or no offer. Experimental outcomes are defined in terms of the results of the three interviews. a.
> The demand for a product of Carolina Industries varies greatly from month to month. The probability distribution in the following table, based on the past two years of data, shows the company’s monthly demand. a. If the company bases
> Consider the experiment of a worker assembling a product. a. Define a random variable that represents the time in minutes required to assemble the product. b. What values may the random variable assume? c. Is the random variable discrete or continuous?
> Establishing Patient Trust. A psychologist determined that the number of sessions required to obtain the trust of a new patient is either 1, 2, or 3. Let x be a random variable indicating the number of sessions required to gain the patientâ€&#
> Spectrum provides cable television and Internet service to millions of customers. Suppose that the management of Spectrum subjectively assesses a probability distribution for the number of new subscribers next year in the state of New York as follows.
> A technician services mailing machines at companies in the Phoenix area. Depending on the type of malfunction, the service call can take 1, 2, 3, or 4 hours. The different types of malfunctions occur at about the same frequency. a. Develop a probability
> The following data are for 30 observations involving two categorical variables, x and y. The categories for x are A, B, and C; the categories for y are 1 and 2. a. Develop a crosstabulation for the data, with x as the row variable and y as the column v
> Consider the experiment of tossing a coin twice. a. List the experimental outcomes. b. Define a random variable that represents the number of heads occurring on the two tosses. c. Show what value the random variable would assume for each of the experimen
> Simple random sampling uses a sample of size n from a population of size N to obtain data that can be used to make inferences about the characteristics of a population. Suppose that, from a population of 50 bank accounts, we want to take a random sample
> A decision maker subjectively assigned the following probabilities to the four outcomes of an experiment: P(E1) = .10, P(E2) = .15, P(E3) = .40, and P(E4) = .20. Are these probability assignments valid? Explain.
> An experiment with three outcomes has been repeated 50 times, and it was learned that E1 occurred 20 times, E2 occurred 13 times, and E3 occurred 17 times. Assign probabilities to the outcomes. What method did you use?
> Suppose an experiment has five equally likely outcomes: E1, E2, E3, E4, E5. Assign probabilities to each outcome and show that the requirements in equations (4.3) and (4.4) are satisfied. What method did you use?
> A local bank reviewed its credit card policy with the intention of recalling some of its credit cards. In the past approximately 5% of cardholders defaulted, leaving the bank unable to collect the outstanding balance. Hence, management established a prio
> A consulting firm submitted a bid for a large research project. The firm’s management initially felt they had a 50–50 chance of getting the project. However, the agency to which the bid was submitted subsequently requested additional information on the b
> Consider the experiment of tossing a coin three times. a. Develop a tree diagram for the experiment. b. List the experimental outcomes. c. What is the probability for each experimental outcome?
> Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = .30 and P(B) = .40. a. What is P(A ∩ B)? b. What is P(A ∣ B)? c. A student in statistics argues that the concepts of mutually exclusive events and in
> The Flying Pig is a marathon (26.2 mile long) running race held every year in Cincinnati, Ohio. Suppose that the following data show the ages for a sample of 40 marathon runners. a. Construct a stretched stem-and-leaf display. b. Which age group had th
> Suppose that we have two events, A and B, with P(A) = .50, P(B) = .60, and P(A ∩ B) = .40. a. Find P(A ∣ B). b. Find P(B ∣ A). c. Are A and B independent? Why or why not?
> How many permutations of three items can be selected from a group of six? Use the letters A, B, C, D, E, and F to identify the items, and list each of the permutations of items B, D, and F.
> Survey on Car Rentals. A survey of magazine subscribers showed that 45.8% rented a car during the past 12 months for business reasons, 54% rented a car during the past 12 months for personal reasons, and 30% rented a car during the past 12 months for bot
> A 2018 Pew Research Center survey (Pew Research website) examined the use of social media platforms in the United States. The survey found that there is a .68 probability that a randomly selected American will use Facebook and a .25 probability that a ra
> Clarkson University surveyed alumni to learn more about what they think of Clarkson. One part of the survey asked respondents to indicate whether their overall experience at Clarkson fell short of expectations, met expectations, or surpassed expectations
> How many ways can three items be selected from a group of six items? Use the letters A, B, C, D, E, and F to identify the items, and list each of the different combinations of three items.
> Refer to the KP&L sample points and sample point probabilities in Tables 4.2 and 4.3. a. The design stage (stage 1) will run over budget if it takes 4 months to complete. List the sample points in the event the design stage is over budget. b. What is
> An experiment has four equally likely outcomes: E1, E2, E3, and E4. a. What is the probability that E2 occurs? b. What is the probability that any two of the outcomes occur (e.g., E1 or E3)? c. What is the probability that any three of the outcomes occur
> The Powerball lottery is played twice each week in 44 states, the District of Columbia, and the Virgin Islands. To play Powerball, a participant must purchase a $2 ticket, select five numbers from the digits 1 through 69, and then select a Powerball numb
> An experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. How many experimental outcomes exist for the entire experiment?
> Consumer Reports evaluates products for consumers. The file CompactSUV contains the data shown in Table 1.8 for 15 compact sports utility vehicles (SUVs) from the 2018 model line (Consumer Reports website): Make—manufacturer Modelâ
> Which companies spend the most money on advertising? Business Insider maintains a list of the top-spending companies. In 2014, Procter & Gamble spent more than any other company, a whopping $5 billion. In second place was Comcast, which spent $3.08 b
> There is a severe shortage of critical care doctors and nurses to provide intensive-care services in hospitals. To offset this shortage, many hospitals, such as Emory Hospital in Atlanta, are using electronic intensive-care units (eICUs) to help provide
> Consider a sample with data values of 53, 55, 70, 58, 64, 57, 53, 69, 57, 68, and 53. Compute the mean, median, and mode.
> A data set has a first quartile of 42 and a third quartile of 50. Compute the lower and upper limits for the corresponding boxplot. Should a data value of 65 be considered an outlier?
> Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.
> Show the boxplot for the data in exercise 46. Data from exercise 46: Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Provide the five-number summary for the data.
> Consider the following data. What is the mean growth rate over these five periods?
> Suppose the data have a bell-shaped distribution with a mean of 30 and a standard deviation of 5. Use the empirical rule to determine the percentage of data within each of the following ranges: a. 20 to 40 b. 15 to 45 c. 25 to 35
> Consider a sample with a mean of 30 and a standard deviation of 5. Use Chebyshev’s theorem to determine the percentage of the data within each of the following ranges: a. 20 to 40 b. 15 to 45 c. 22 to 38 d. 18 to 42 e. 12 to 48
> Consider a sample with a mean of 500 and a standard deviation of 100. What are the z-scores for the following data values: 520, 650, 500, 450, and 280?
> A sample of midterm grades for five students showed the following results: 72, 65, 82, 90, 76. Which of the following statements are correct, and which should be challenged as being too generalized? a. The average midterm grade for the sample of five stu
> Many families in California are using backyard structures for home offices, art studios, and hobby areas as well as for additional storage. Suppose that the mean price for a customized wooden, shingled backyard structure is $3100. Assume that the standar
> Consider the following data and corresponding weights. a. Compute the weighted mean. b. Compute the sample mean of the four data values without weighting. Note the difference in the results provided by the two computations.
> The current value of a company is $25 million. If the value of the company six year ago was $10 million, what is the company’s mean annual growth rate over the past six years?
> A study on driving speed (miles per hour) and fuel efficiency (miles per gallon) for midsize automobiles resulted in the following data: a. Construct a scatter diagram with driving speed on the horizontal axis and fuel efficiency on the vertical axis.
> The following crosstabulation summarizes the data for two categorical variables, x and y. The variable x can take on values low, medium, or high and the variable y can take on values yes or no. a. Compute the row percentages. b. Construct a stacked per
> Consider the following data on two categorical variables. The first variable, x, can take on values A, B, C, or D. The second variable, y, can take on values I or II. The following table gives the frequency with which each combination occurs. a. Constr
> The following 20 observations are for two quantitative variables, x and y. a. Develop a scatter diagram for the relationship between x and y. b. What is the relationship, if any, between x and y?
> Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the z-score for each of the five observations.
> The following times were recorded by the quarter- mile and mile runners of a university track team (times are in minutes). After viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent ti
> If an asset declines in value from $5000 to $3500 over nine years, what is the mean annual growth rate in the asset’s value over these nine years?
> Pew Research Center is a nonpartisan polling organization that provides information about issues, attitudes, and trends shaping America. In a poll, Pew researchers found that 73% of teens aged 13–17 have a smartphone, 15% have a basic phone and 12% ha
> Consider a sample with data values of 10, 20, 21, 17, 16, and 12. Compute the mean and median.
> According to the 2016 Consumer Expenditure Survey, Americans spend an average of $1124 on cellular phone service annually (U.S. Bureau of Labor Statistics website). Suppose that we wish to determine if there are differences in cellular phone expenditures
> The following data were used to construct the histograms of the number of days required to fill orders for Dawson Supply, Inc., and J.C. Clark Distributors Use the range and standard deviation to support the previous observation that Dawson Supply prov
> The Los Angeles Times regularly reports the air quality index for various areas of Southern California. A sample of air quality index values for Pomona provided the following data: 28, 42, 58, 48, 45, 55, 60, 49, and 50. a. Compute the range and interqua
> Annual revenue for Corning Supplies grew by 5.5% in 2014, 1.1% in 2015, −3.5% in 2016, −1.1% in 2017, and 1.8% in 2018. What is the mean growth annual rate over this period?
> Based on a survey of master’s programs in business administration, magazines such as U.S. News & World Report rank U.S. business schools. These types of rankings are based in part on surveys of business school deans and corporate re
> The grade point average for college students is based on a weighted mean computation. For most colleges, the grades are given the following data values: A (4), B (3), C (2), D (1), and F (0). After 60 credit hours of course work, a student at State Unive
> Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the mean and median.
> Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the variance and standard deviation.
> Consider a sample with data values of 10, 20, 12, 17, and 16. Compute the range and interquartile range.
> A survey conducted by Better Homes and Gardens Real Estate LLC showed that one in five U.S. homeowners has either moved from their home or would like to move because their neighborhood or community isn’t ideal for their lifestyle (Better Homes and Garden
> Construct a stem-and-leaf display for the following data. Use a leaf unit of 10.
> Construct a stem-and-leaf display for the following data.
> Construct a histogram for the data in exercise 12. Data from exercise 12:
> Consider the following data. a. Develop a frequency distribution using classes of 12–14, 15–17, 18–20, 21–23, and 24–26. b. Develop a relative frequency distribut
> A random telephone survey of 1021 adults (aged 18 and older) was conducted by Opinion Research Corporation on behalf of CompleteTax, an online tax preparation and e-filing service. The survey results showed that 684 of those surveyed planned to file thei
