Suppose that a particular NBA player makes 93% of his free throws. Assume that late in a basketball game, this player is fouled and is awarded two shots. a. What is the probability that he will make both shots? b. What is the probability that he will make at least one shot? c. What is the probability that he will miss both shots? d. Late in a basketball game, a team often intentionally fouls an opposing player in order to stop the game clock. The usual strategy is to intentionally foul the other team’s worst free-throw shooter. Assume that the the team’s worst free-throw shooter makes 58% of his free-throw shots. Calculate the probabilities for this player as shown in parts (a), (b), and (c), and show that intentionally fouling this player who makes 58% of his free throws is a better strategy than intentionally fouling the player who makes 93% of his free throws. Assume as in parts (a), (b), and (c) that two shots will be awarded.
> 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
> 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
> In the city of Milford, applications for zoning changes go through a two-step process: a review by the planning commission and a final decision by the city council. At step 1 the planning commission reviews the zoning change request and makes a positive
> 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?
> The National Center for Health Statistics, housed within the U.S. Centers for Disease Control and Prevention (CDC), tracks the number of adults in the United States who have health insurance. According to this agency, the uninsured rates for Americans in
> ParFore created a website to market golf equipment and golf apparel. Management would like a special pop-up offer to appear for female website visitors and a different special pop-up offer to appear for male website visitors. From a sample of past websit
> According to a 2018 article in Esquire magazine, approximately 70% of males over age 70 will develop cancerous cells in their prostate. Prostate cancer is second only to skin cancer as the most common form of cancer for males in the United States. One of
> According to USC Annenberg, the mean time spent by Americans on the Internet in their home per week is 17.6 hours. Assume that the standard deviation for the time spent by Americans on the Internet in their home per week is 5.1 hours. Suppose the Florida
> 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
> The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The conditional probabilities of event B given A1, A2, and A3 are P(B ∣ A1) = .50, P(B ∣ A2) = .40, and P(B ∣ A3) = .30. a. Compute P(B ∩ A1), P(B ∩ A2), and
> 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?
> 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
> The Institute for Higher Education Policy, a Washington, D.C.-based research firm, studied the payback of student loans for 1.8 million college students who had student loans that began to become due six years ago (The Wall Street Journal). The study fou
> A 2018 Pew Research Center survey found that more Americans believe they could give up their televisions than could give up their cell phones (Pew Research website). Assume that the following table represents the joint probabilities of Americans who coul
> To better understand how husbands and wives feel about their finances, Money magazine conducted a national poll of 1010 married adults age 25 and older with household incomes of $50,000 or more (Money website). Consider the following example set of resp
> The Bureau of Transportation Statistics reports on-time performance for airlines at major U.S. airports. JetBlue, United, and US Airways share terminal C at Boston’s Logan Airport. Suppose that the percentage of on-time flights reported was 76.8% for Jet
> In 2018, the Simple Dollar website reported that the mean life of 14-watt compact fluorescent lights (CFLs) is 8000 hours. Assume that for this population the standard deviation for CFL life is 480. Suppose the U.S. Department of Energy would like to sel
> Students taking the Graduate Management Admissions Test (GMAT) were asked about their undergraduate major and intent to pursue their MBA as a full-time or part-time student. A summary of their responses follows. a. Develop a joint probability table for
> Consider the following example survey results of 18- to 34-yearolds in the United States, in response to the question “Are you currently living with your family?” a. Develop the joint probability table for these data
> 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
> 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.
> High school seniors with strong academic records apply to the nation’s most selective colleges in greater numbers each year. Because the number of slots remains relatively stable, some colleges reject more early applicants. Suppose that for a recent admi
> 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 both business and personal
> A marketing firm would like to test-market the name of a new energy drink targeted at 18- to 29-year-olds via social media. A study by the Pew Research Center found that 35% of U.S. adults (18 and older) do not use social media (Pew Research Center websi
> Information about mutual funds provided by Morningstar includes the type of mutual fund (Domestic Equity, International Equity, or Fixed Income) and the Morningstar rating for the fund. The rating is expressed from 1-star (lowest rating) to 5-star (highe
> 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
> Lori Jeffrey is a successful sales representative for a major publisher of college textbooks. Historically, Lori obtains a book adoption on 25% of her sales calls. Viewing her sales calls for one month as a sample of all possible sales calls, assume that
> 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
> Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, . . . , E7 denote the sample points. The following probability assignments apply: P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7)
> Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Let A = {E1, E2} B = {E3, E4} C = {E2, E3, E5} a. Find P(A), P(B), and P(C). b. Find P(A ∪ B). Are A and B mutually exclusive? c. Find Ac, Cc, P(Ac),
> The National Highway Traffic Safety Administration (NHTSA) collects traffic safety-related data for the U.S. Department of Transportation. According to NHTSA’s data, 10,426 fatal collisions in 2016 were the result of collisions with fixed objects (NHTSA
> Suppose that the following table represents a sample of 944 teenagers’ responses to the question, “When do you think you will become financially independent?” Age of Financially Independent …………………….. Number of Responses 16 to 20 ……………………………………………………………
> 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.
> Do you think global warming will have an impact on you during your lifetime? A 2014 CBS News/New York Times poll of 1000 adults in the United States asked this question (CBS News website). Consider the responses by age groups shown below. a. What is th
> Each year Fortune magazine publishes an annual list of the 500 largest companies in the United States. The corporate headquarters for the 500 companies are located in 38 different states. The following table shows the 8 states with the largest number of
> 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
> Consider the experiment of rolling a pair of dice. Suppose that we are interested in the sum of the face values showing on the dice. a. How many sample points are possible? b. List the sample points. c. What is the probability of obtaining a value of 7?
> The proportion of individuals insured by the All-Driver Automobile Insurance Company who received at least one traffic ticket during a five-year period is .15. a. Show the sampling distribution of p̅ if a random sample of 150 insured individuals is used
> Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a 1/52 probability. a. List the sample points in the event an ace is selected. b. List the sample points in the event a club
> 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
> A company that manufactures toothpaste is studying five different package designs. Assuming that one design is just as likely to be selected by a consumer as any other design, what selection probability would you assign to each of the package designs? In
> A Gallup Poll of U.S. adults indicated that Kentucky is the state with the highest percentage of smokers (Gallup website). Consider the following example data from the Tri-State region, an area that comprises northern Kentucky, southeastern Indiana, and
> Code Churn is a common metric used to measure the efficiency and productivity of software engineers and computer programmers. It’s usually measured as the percentage of a programmer’s code that must be edited over a sh
> 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?
> 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
> Suppose that an independent study of middle-level managers employed at companies located in Atlanta, Georgia, was conducted to compare the salaries of managers working at firms in Atlanta to the salaries of middle-level managers across the nation. The fo
> 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
> Advertisers contract with Internet service providers and search engines to place ads on websites. They pay a fee based on the number of potential customers who click on their ad. Unfortunately, click fraud—the practice of someone clicking on an ad solely
> 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.
> Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the 20th, 25th, 65th, and 75th percentiles.
> Each year Money magazine publishes a list of “Best Places to Live in the United States.” These listings are based on affordability, educational performance, convenience, safety, and livability. The list below shows the
> 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
> The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped
> Suppose that the mean retail price per gallon of regular grade gasoline in the United States is $3.43 with a standard deviation of $.10 and that the retail price per gallon has a bell-shaped distribution. a. What percentage of regular grade gasoline sold
> Consider the following data. Period Rate …………………………………… of Return (%) 1 ………………………………………………………………… 26.0 2 ………………………………………………………………… 28.0 3 ………………………………………………………………… 24.0 4 ……………………………………………………………….… 2.0 5 ………………………………………………………………….. 5.4 What is the mean
> The results of a national survey showed that on average, adults sleep 6.9 hours per night. Suppose that the standard deviation is 1.2 hours. a. Use Chebyshev’s theorem to calculate the percentage of individuals who sleep between 4.5 and 9.3 hours. b. Use
> 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
> A market research firm conducts telephone surveys with a 40% historical response rate. What is the probability that in a new sample of 400 telephone numbers, at least 150 individuals will cooperate and respond to the questions? In other words, what is th
> 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?
> 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
> Scores turned in by an amateur golfer at the Bonita Fairways Golf Course in Bonita Springs, Florida, during 2017 and 2018 are as follows: a. Use the mean and standard deviation to evaluate the golfer’s performance over the two-year pe
