Comcast Corporation is a global telecommunications company headquartered in Philadelphia, PA. Generally known for reliable service, the company periodically experiences unexpected service interruptions. When service interruptions do occur, Comcast customers who call the office receive a message providing an estimate of when service will be restored. Suppose that for a particular outage, Comcast customers are told that service will be restored in two hours. Assume that two hours is the mean time to do the repair and that the repair time has an exponential probability distribution. a. What is the probability that the cable service will be repaired in one hour or less? b. What is the probability that the repair will take between one hour and two hours? c. For a customer who calls the Comcast office at 1:00 p.m., what is the probability that the cable service will not be repaired by 5:00 p.m.?
> Data made available through the Petersen-Kaiser Health System Tracker in May 2018 showed health expenditures were $10,348 per person in the United States. Use $10,348 as the population mean and suppose a survey research firm will take a sample of 100 peo
> The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population. a. Show the sampling distribution of p̅
> The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product’s label. Assume the population proportion is p = .76 and a sample of 400 consumers is selected from the population. a. Show the sampling distribu
> The 10 most active stocks on the New York Stock Exchange for a given week, are shown here. Exchange authorities decided to investigate trading practices using a sample of three of these stocks. a. Beginning with the first random digit in column 6 of Ta
> In 2016 the Better Business Bureau settled 80% of complaints they received in the United States. Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select
> According to Reader’s Digest, 42% of primary care doctors think their patients receive unnecessary medical care. a. Suppose a sample of 300 primary care doctors was taken. Show the sampling distribution of the proportion of the doctors who think their pa
> In 2017, the Restaurant Hospitality website reported that only 10% of surplus food is being recovered in the food-service and restaurant sector, leaving approximately 1.5 billion meals per year uneaten. Assume this is the true population proportion and t
> The Wall Street Journal reported that the age at first startup for 55% of entrepreneurs was 29 years of age or less and the age at first startup for 45% of entrepreneurs was 30 years of age or more. a. Suppose a sample of 200 entrepreneurs will be taken
> The president of Doerman Distributors, Inc., believes that 30% of the firm’s orders come from first-time customers. A random sample of 100 orders will be used to estimate the proportion of first-time customers. a. Assume that the president is correct and
> The population proportion is .30. What is the probability that a sample proportion will be within ±.04 of the population proportion for each of the following sample sizes? a. n = 100 b. n = 200 c. n = 500 d. n = 1000 e. What is the advantage of a larger
> Assume that the population proportion is .55. Compute the standard error of the proportion, σp̅, for sample sizes of 100, 200, 500, and 1000. What can you say about the size of the standard error of the proportion as the sample size is increased?
> 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 population proportion is .40. A sample of size 200 will be taken and the sample proportion p̅ will be used to estimate the population proportion. a. What is the probability that the sample proportion will be within ±.03 of the population proportion? b.
> A sample of size 100 is selected from a population with p̅ = .40. a. What is the expected value of p̅ ? b. What is the standard error of p̅ ? c. Show the sampling distribution of p̅. d. What does the sampling distribution of p̅ show?
> To estimate the mean age for a population of 4000 employees, a simple random sample of 40 employees is selected. a. Would you use the finite population correction factor in calculating the standard error of the mean? Explain. b. If the population standar
> 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
> The CPA Practice Advisor reports that the mean preparation fee for 2017 federal income tax returns was $273. Use this price as the population mean and assume the population standard deviation of preparation fees is $100. a. What is the probability that t
> The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a
> The Economic Policy Institute periodically issues reports on worker’s wages. The institute reported that mean wages for male college graduates were $37.39 per hour and for female college graduates were $27.83 per hour in 2017. Assume the standard deviati
> The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $16,642. Assume the s
> In May 2018, The College Board reported the following mean scores for two parts of the Scholastic Aptitude Test (SAT): Assume that the population standard deviation on each part of the test is s = 100. a. What is the probability a sample of 90 test tak
> Barron’s reported that the average number of weeks an individual is unemployed is 17.5 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 17.5 weeks and that the population standard deviation
> TripAdvisor is one of many online websites that provides ratings for hotels throughout the world. Ratings provided by 649 guests at the Lakeview Hotel can be found in the file HotelRatings. Possible responses were Excellent, Very Good, Average, Poor, and
> In the EAI sampling problem (see Figure 7.5), we showed that for n = 30, there was .5034 probability of obtaining a sample mean within ±$500 of the population mean. a. What is the probability that x̅ is within $500 of the popul
> Refer to the EAI sampling problem. Suppose a simple random sample of 60 managers is used. a. Sketch the sampling distribution of x̅ when simple random samples of size 60 are used. b. What happens to the sampling distribution of x̅ if simple random sample
> Suppose a random sample of size 50 is selected from a population with σ = 10. Find the value of the standard error of the mean in each of the following cases (use the finite population correction factor if appropriate). a. The population size is infinite
> Assume the population standard deviation is σ = 25. Compute the standard error of the mean, σx̅, 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?
> Assume a finite population has 350 elements. Using the last three digits of each of the following five-digit random numbers (e.g., 601, 022, 448, . . . ), determine the first four elements that will be selected for the simple random sample.
> A population has a mean of 200 and a standard deviation of 50. Suppose a sample of size 100 is selected and x̅ is used to estimate µ. a. What is the probability that the sample mean will be within ±5 of the population mean? b. What is the probability tha
> A population has a mean of 200 and a standard deviation of 50. A sample of size 100 will be taken and the sample mean x̅ will be used to estimate the population mean. a. What is the expected value of x̅ ? b. What is the standard deviation of x̅ ? c. Show
> 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
> In a sample of 426 U.S. adults age 50 and older, AARP asked how important a variety of issues were in choosing whom to vote for in the next presidential election. a. What is the sampled population for this study? b. Social Security and Medicare was cited
> 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€
> Nearly 1.9 million bachelor’s degrees and over 758,000 master’s degrees are awarded annually by U.S. postsecondary institutions as of 2018 (National Center for Education Statistics website). The Department of Education
> 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
> 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. a. What is the point estimate of the population mean? b. What is the point estimate of the population standard deviation?
> Indicate which of the following situations involve sampling from a finite population and which involve sampling from an infinite population. In cases where the sampled population is finite, describe how you would construct a frame. a. Obtain a sample of
> 1. Consider a finite population with five elements labeled A, B, C, D, and E. Ten possible simple random samples of size 2 can be selected. a. List the 10 samples beginning with AB, AC, and so on. b. Using simple random sampling, what is the probability
> A random variable is normally distributed with a mean of µ = 50 and a standard deviation of σ = 5. a. Sketch a normal curve for the probability density function. Label the horizontal axis with values of 35, 40, 45, 50, 55, 60, and 65. Figure 6.6 shows th
> Using Figure 6.6 as a guide, sketch a normal curve for a random variable x that has a mean of µ = 100 and a standard deviation of σ = 10. Label the horizontal axis with values of 70, 80, 90, 100, 110, 120, and 130. Figure 6.6:
> Suppose we are interested in bidding on a piece of land and we know one other bidder is interested.1 The seller announced that the highest bid in excess of $10,000 will be accepted. Assume that the competitor’s bid x is a random variable that is uniforml
> A Gallup Daily Tracking Survey found that the mean daily discretionary spending by Americans earning over $90,000 per year was $136 per day. The discretionary spending excluded home purchases, vehicle purchases, and regular monthly bills. Let x 5 the dis
> Data for a sample of 55 members of the Baseball Hall of Fame in Cooperstown, New York, are shown here. Each observation indicates the primary position played by the Hall of Famers: pitcher (P), catcher (H), 1st base (1), 2nd base (2), 3rd base (3), short
> 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)
> Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous ra
> The Boston Fire Department receives 911 calls at a mean rate of 1.6 calls per hour (Mass.gov website). Suppose the number of calls per hour follows a Poisson probability distribution. a. What is the mean time between 911 calls to the Boston Fire Departme
> Intensive care units (ICUs) generally treat the sickest patients in a hospital. ICUs are often the most expensive department in a hospital because of the specialized equipment and extensive training required to be an ICU doctor or nurse. Therefore, it is
> The time between arrivals of vehicles at a particular intersection follows an exponential probability distribution with a mean of 12 seconds. a. Sketch this exponential probability distribution. b. What is the probability that the arrival time between ve
> Battery life between charges for a certain mobile phone is 20 hours when the primary use is talk time, and drops to 7 hours when the phone is primarily used for Internet applications over a cellular network. Assume that the battery life in both cases fol
> Consider the following exponential probability density function. f (x) = 1/3 e-x/3 for x ≥ 0 a. Write the formula for P(x ≤ x0). b. Find P(x ≤ 2). c. Find P(x ≥ 3). d. Find P(x ≤ 5). e. Find P(2 ≤ x ≤ 5).
> Consider the following exponential probability density function. f (x) = 1/8 e-x /8 for x ≥ 0 a. Find P(x ≤ 6). b. Find P(x ≤ 4). c. Find P(x ≥ 6). d. Find P(4 ≤ x ≤ 6).
> Rocky Mountain National Park is a popular park for outdoor recreation activities in Colorado. According to U.S. National Park Service statistics, 46.7% of visitors to Rocky Mountain National Park in 2018 entered through the Beaver Meadows park entrance,
> Many airlines use surveys to collect data on customer satisfaction related to flight experiences. Completing a flight, customers receive an email asking them to rate a variety of factors, including the reservation process, the check-in process, luggage p
> Suppose that of those individuals who play video and computer games, 18% are under 18 years old, 53% are 18–59 years old, and 29% are over 59 years old. Use the normal approximation of the binomial distribution to answer the questions below. a. For a sam
> 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
> According to a Yale program on climate change communication survey, 71% of Americans think global warming is happening (American Psychological Association website). a. For a sample of 15 Americans, what is the probability that at least 12 believe global
> Although studies continue to show smoking leads to significant health problems, 20% of adults in the United States smoke. Consider a group of 250 adults, and use the normal approximation of the binomial distribution to answer the questions below. a. What
> Assume a binomial probability distribution has p = .60 and n = 200. a. What are the mean and standard deviation? b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. c. What is the
> A binomial probability distribution has p = .20 and n = 100. a. What are the mean and standard deviation? b. Is this situation one in which binomial probabilities can be approximated by the normal probability distribution? Explain. c. What is the probabi
> According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847 (Time.com website). Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard d
> The American Automobile Association (AAA) reported that families planning to travel over the Labor Day weekend spend an average of $749. Assume that the amount spent is normally distributed with a standard deviation of $225. a. What is the probability of
> The time needed to complete a final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes. Answer the following questions. a. What is the probability of completing the exam in
> Suppose that the mean daily viewing time of television is 8.35 hours. Use a normal probability distribution with a standard deviation of 2.5 hours to answer the following questions about daily television viewing per household. a. What is the probability
> Nielsen Media Research tracks the top-rated television shows. The following data show the television network that produced each of the 25 top-rated shows in the history of television. a. Construct a frequency distribution, percent frequency distributio
> 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
> Suppose that the average price for a gallon of gasoline in the United States is $3.73 and in Russia is $3.40. Assume these averages are the population means in the two countries and that the probability distributions are normally distributed with a stand
> 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).
> Automobile repair costs continue to rise with an average 2015 cost of $367 per repair (U.S. News & World Report website). Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. Answer the following questio
> The average return for large-cap domestic stock funds over the three years was 14.4%. Assume the three-year returns were normally distributed across funds with a standard deviation of 4.4%. a. What is the probability an individual large-cap domestic stoc
> Males in the Netherlands are the tallest, on average, in the world with an average height of 183 centimeters (cm) (BBC News website). Assume that the height of men in the Netherlands is normally distributed with a mean of 183 cm and standard deviation of
> Given that z is a standard normal random variable, find z for each situation. a. The area to the right of z is .01. b. The area to the right of z is .025. c. The area to the right of z is .05. d. The area to the right of z is .10.
> Given that z is a standard normal random variable, find z for each situation. a. The area to the left of z is .2119. b. The area between −z and z is .9030. c. The area between −z and z is .2052. d. The area to the left of z is .9948. e. The area to the r
> Given that z is a standard normal random variable, find z for each situation. a. The area to the left of z is .9750. b. The area between 0 and z is .4750. c. The area to the left of z is .7291. d. The area to the right of z is .1314. e. The area to the l
> Given that z is a standard normal random variable, compute the following probabilities. a. P(−1.98 ≤ z ≤ .49) b. P(.52 ≤ z ≤ 1.22) c. P(−1.75 ≤ z ≤ −1.04)
> In alphabetical order, the six most common last names in the United States in 2018 are Brown, Garcia, Johnson, Jones, Smith, and Williams (United States Census Bureau website). Assume that a sample of 50 individuals with one of these last names provided
> Given that z is a standard normal random variable, compute the following probabilities. a. P(0 ≤ z ≤ .83) b. P(−1.57 ≤ z ≤ 0) c. P(z > .44) d. P(z ≥ −.23) e. P(z < 1.20) f. P(z ≤ −.71)
> Given that z is a standard normal random variable, compute the following probabilities. a. P(z ≤ −1.0) b. P(z ≥ −1) c. P(z ≥ −1.5) d. P(−2.5 ≤ z) e. P(−3 < z ≤ 0)
> 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).
> 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
> The probability distribution for the random variable x follows. x ……………………. f(x) 20 …………………… .20 25 ……………………. .15 30 …………………… .25 35 …………………… .40 a. Is this probability distribution valid? Explain. b. What is the probability that x = 30? c. What is the
> 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. Experiment …………………………………………………….……………………… Ran
> The Troubled Asset Relief Program (TARP), passed by the U.S. Congress in October 2008, provided $700 billion in assistance for the struggling U.S. economy. Over $200 billion was given to troubled financial institutions with the hope that there would be a
> 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
> In a recent report, the top five most-visited English-language websites were google.com (GOOG), facebook.com (FB), youtube.com (YT), yahoo. com (YAH), and wikipedia.com (WIKI). The most-visited websites for a sample of 50 Internet users are shown in the
> Axline Computers manufactures personal computers at two plants, one in Texas and the other in Hawaii. The Texas plant has 40 employees; the Hawaii plant has 20. A random sample of 10 employees is to be asked to fill out a benefits questionnaire. a. What
> Blackjack, or twenty-one as it is frequently called, is a popular gambling game played in casinos. A player is dealt two cards. Face cards (jacks, queens, and kings) and tens have a point value of 10. Aces have a point value of 1 or 11. A 52-card deck co
> 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?
> Suppose N = 10 and r = 3. Compute the hypergeometric probabilities for the following values of n and x. a. n = 4, x = 1. b. n = 2, x = 2. c. n = 2, x = 0. d. n = 4, x = 2. e. n = 4, x = 4.
> 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
> Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 10 passengers per minute. a. Compute the probability of no arrivals in a one-minute period. b. Compute the
> In a one-year period, New York City had a total of 11,232 motor vehicle accidents that occurred on Monday through Friday between the hours of 3 p.m. and 6 p.m. (New York State Department of Motor Vehicles website). This corresponds to mean of 14.4 accide
> A questionnaire provides 58 Yes, 42 No, and 20 no-opinion answers. a. In the construction of a pie chart, how many degrees would be in the section of the pie showing the Yes answers? b. How many degrees would be in the section of the pie showing the No a
> 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
