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 of no tornadoes during a day. c. Compute the probability of exactly one tornado during a day. d. Compute the probability of more than one tornado during a day.
> 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
> 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 custom
> 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
> 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
> Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways. a. Compute the probability of receiving three calls in a 5-minute interval of time. b. Compute the probability of receiving exactly 10 calls in 15 minutes. c. Sup
> Consider a Poisson distribution with a mean of two occurrences per time period. a. Write the appropriate Poisson probability function. b. What is the expected number of occurrences in three time periods? c. Write the appropriate Poisson probability funct
> Consider a Poisson distribution with µ = 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
> Suppose a sample of 20 Americans is selected as part of a study of the state of the nation. The Americans in the sample are asked whether or not they are satisfied with the way things are going in the United States. a. Compute the probability that exactl
> 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
> Suppose that a random sample of fifteen 18- to 34-year-olds living with their parents is selected and asked if they contribute to household expenses. a. Is the selection of the fifteen 18- to 34-year-olds living with their parents a binomial experiment?
> 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
> Market-share-analysis company Net Applications monitors and reports on Internet browser usage. According to Net Applications, in the summer of 2014, Google’s Chrome browser exceeded a 20% market share for the first time, with a 20.37% share of the browse
> A partial relative frequency distribution is given. a. What is the relative frequency of class D? b. The total sample size is 200. What is the frequency of class D? c. Show the frequency distribution. d. Show the percent frequency distribution. Class Re
> Jack Lawler, a financial analyst, wants to prepare an article on the Shadow Stock portfolio developed by the American Association of Individual Investors (AAII). A list of the 30 companies in the Shadow Stock portfolio is contained in the file ShadowStoc
> Military radar and missile detection systems are designed to warn a country of an enemy attack. A reliability question is whether a detection system will be able to identify an attack and issue a warning. Assume that a particular detection system has a .
> According to a 2018 survey by Bankrate.com, 20% of adults in the United States save nothing for retirement (CNBC website). Suppose that 15 adults in the United States are selected randomly. a. Is the selection of the 15 adults a binomial experiment? Expl
> When a new machine is functioning properly, only 3% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found. a. Describe the conditions u
> The Center for Medicare and Medical Services reported that there were 295,000 appeals for hospitalization and other Part A Medicare service. For this group, 40% of first-round appeals were successful (The Wall Street Journal). Suppose 10 first-round appe
> For its Music 360 survey, Nielsen Co. asked teenagers and adults how each group has listened to music in the past 12 months. Nearly two-thirds of U.S. teenagers under the age of 18 say they use Google Inc.’s video-sharing site to listen to music and 35%
> Consider a binomial experiment with n = 20 and p = .70. a. Compute f (12). b. Compute f (16). c. Compute P(x ≥ 16). d. Compute P(x ≤ 15). e. Compute E(x). f. Compute Var (x) and σ.
> Consider a binomial experiment with n = 10 and p = .10. a. Compute f (0). b. Compute f (2). c. Compute P(x ≤ 2). d. Compute P(x ≥ 1). e. Compute E(x). f. Compute Var(x) and σ.
> Consider a binomial experiment with two trials and p = .4. a. Draw a tree diagram for this experiment (see Figure 5.3). b. Compute the probability of one success, f (1). c. Compute f (0). d. Compute f (2). e. Compute the probability of at least one succe
> In addition to the information in exercise 29 on the S&P 500 and core bonds, J.P. Morgan Asset Management reported that the expected return for real estate investment trusts (REITs) during the same time period was 13.07% with a standard deviation of 23.1
> 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 response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 60 A, 24 B, and 36 C. Show the frequency and relative frequency distributions.
> J.P. Morgan Asset Management publishes information about financial investments. Between 2002 and 2011, the expected return for the S&P 500 was 5.04% with a standard deviation of 19.45% and the expected return over that same period for a core bonds fund w
> PortaCom has developed a design for a high-quality portable printer. The two key components of manufacturing cost are direct labor and parts. During a testing period, the company has developed prototypes and conducted extensive product tests with the new
> The Chamber of Commerce in a Canadian city has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received a rating on a 3-point scale on typical meal price (1 least expensive to 3 most expensive) and quality (1 lowest q
> A person is interested in constructing a portfolio. Two stocks are being considered. Let x = percent return for an investment in stock 1, and y = percent return for an investment in stock 2. The expected return and variance for stock 1 are E(x) = 8.45% a
> Given below is a bivariate distribution for the random variables x and y. a. Compute the expected value and the variance for x and y. b. Develop a probability distribution for x + y. c. Using the result of part (b), compute E(x + y) and Var (x + y). d.
> The J. R. Ryland Computer Company is considering a plant expansion to enable the company to begin production of a new computer product. The company’s president must determine whether to make the expansion a medium- or large-scale projec
> In Gallup’s Annual Consumption Habits Poll, telephone interviews were conducted for a random sample of 1014 adults aged 18 and over. One of the questions was, “How many cups of coffee, if any, do you drink on an average day?” The following table shows th
> 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. Unit Demand ……………… Probability 300 ……………………
> The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied). a. What is the expected value o
> The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows. Payment ($) ………………………………… Probability 0 ………………………………………………………….. .85 500 …………………………………………………….… .04 1000 ………………………………………………..…
> ABC News reports that 58% of U.S. drivers admit to speeding. Suppose that a new satellite technology can instantly measure the speed of any vehicle on a U.S. road and determine whether the vehicle is speeding, and this satellite technology was used to ta
> 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?
> New legislation passed in 2017 by the U.S. Congress changed tax laws that affect how many people file their taxes in 2018 and beyond. These tax law changes will likely lead many people to seek tax advice from their accountants (The New York Times). Backe
> The following data has been collected on the number of times that owner-occupied and renter-occupied units had a water supply stoppage lasting 6 or more hours in the past 3 months. a. Define a random variable x = number of times that owner-occupied uni
> During the summer of 2018, Coldstream Country Club in Cincinnati, Ohio, collected data on 443 rounds of golf played from its white tees. The data for each golfer’s score on the twelfth hole are contained in the DATAfile Coldstream12. a. Construct an empi
> The following table provides a probability distribution for the random variable y. y ……………… f (y) 2 ……………… .20 4 ……………… .30 7 ……………… .40 8 ……………… .10 a. Compute E( y). b. Compute Var( y) and σ.
> The following table provides a probability distribution for the random variable x. x ……………… f(x) 3 ……………… .25 6 ……………… .50 9 ……………… .25 a. Compute E(x), the expected value of x. b. Compute σ2, the variance of x. c. Compute σ, the standard deviation of
> The following table is a partial probability distribution for the MRA Company’s projected profits (x = profit in $1000s) for the first year of operation (the negative value denotes a loss). x ……………………….………………… f(x) −100 ………………….…………………. .10 0 ……………………….
> 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 patient’s trust. The following probability functio
> 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. x
> 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
> Of the 155 billion mailpieces the U.S. Postal Service (USPS) processed and delivered in 2017, 4.3% were undeliverable as addressed. Suppose that a brief questionnaire about USPS service is attached to each mailpiece in a random sample of 114,250 mailpiec
> The percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and middle managers are as follows. The scores range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied). a. Devel
> 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
