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essentials of statistics

Questions and Answers of Essentials Of Statistics

40. 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
39. 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
38. 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).
37. Twenty-three percent of automobiles are not covered by insurance (CNN, February 23, 2006). On a particular weekend, 35 automobiles are involved in traffic accidents.a. What is the expected number
36. According to a survey conducted by TD Ameritrade, one out of four investors have exchange-traded funds in their portfolios (USA Today, January 11, 2007). For a sample of 20 investors, answer the
35. 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 two
34. The Census Bureau’s Current Population Survey shows 28% of individuals, ages 25 and older, have completed four years of college (The New York Times Almanac, 2006). For a sample of 15
33. Fifty percent of Americans believed the country was in a recession, even though technically the economy had not shown two straight quarters of negative growth (BusinessWeek, July 30, 2001). For a
32. 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
31. Nine percent of undergraduate students carry credit card balances greater than $7000(Reader’s Digest, July 2002). Suppose 10 undergraduate students are selected randomly to be interviewed about
30. 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
29. In San Francisco, 30% of workers take public transportation daily (USA Today, December 21, 2005).a. In a sample of 10 workers, what is the probability that exactly three workers take public
28. AHarris Interactive survey for InterContinental Hotels & Resorts asked respondents, “When traveling internationally, do you generally venture out on your own to experience culture, or stick
27. 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.
26. 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.
25. 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
24. 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
23. The 2002 New York City Housing and Vacancy Survey showed a total of 59,324 rentcontrolled housing units and 236,263 rent-stabilized units built in 1947 or later. For these rental units, the
22. 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
21. The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers range from a low of 1 (very dissatisfied) to a
20. The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.a. Use the expected collision payment to determine the collision
19. The National Basketball Association (NBA) records a variety of statistics for each team.Two of these statistics are the percentage of field goals made by the team and the percentage of
18. TheAmericanHousingSurveyreportedthefollowingdataonthenumberofbedroomsinowneroccupied and renter-occupied houses in central cities (http://www.census.gov, March 31, 2003).a. Define a random
17. A volunteer ambulance service handles 0 to 5 service calls on any given day. The probability distribution for the number of service calls is as follows.a. What is the expected number of service
16. The following table provides a probability distribution for the random variable y.a. Compute E( y).b. Compute Var( y) and σ.
15. The following table provides a probability distribution for the random variable x.a. Compute E(x), the expected value of x.b. Compute σ2 , the variance of x.c. Compute σ, the standard deviation
12. The nation’s two biggest cable providers are Comcast Cable Communications, with 21.5 million subscribers, and Time Warner Cable, with 11.0 million subscribers (The New York Times 2007 Almanac).
12. The nation’s two biggest cable providers are Comcast Cable Communications, with 21.5 million subscribers, and Time Warner Cable, with 11.0 million subscribers (The New York Times 2007 Almanac).
11. 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
10. Table 5.4 shows the percent frequency distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers. The scores range from a low of 1
9. Nationally, 38% of fourth-graders cannot read an age-appropriate book. The following data show the number of children, by age, identified as learning disabled under special education. Most of
8. 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
7. The probability distribution for the random variable x follows.a. Is this probability distribution valid? Explain.b. What is the probability that x 30?c. What is the probability that x is less
6. Listed 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
5. 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
4. In November the U.S. unemployment rate was 4.5% (USA Today, January 4, 2007). The Census Bureau includes nine states in the Northeast region. Assume that the random variable of interest is the
3. 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
2. 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
1. 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
60. Companies that do business over the Internet can often obtain probability information about Web site visitors from previous Web sites visited. The article “Internet Marketing”(Interfaces,
59. An oil company purchased an option on land in Alaska. Preliminary geologic studies assigned the following prior probabilities.a. What is the probability of finding oil?b. After 200 feet of
58. A survey conducted by the Pew Internet & American Life Project showed that 8% of Internet users age 18 and older report keeping a blog. Referring to the 18–29 age group as young adults, the
57. A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical records show that 6% of the employees suffered lost-time accidents last year. Management
56. Cooper Realty is a small real estate company located in Albany, New York, specializing primarily in residential listings. They recently became interested in determining the likelihood of one of
55. A large consumer goods company ran a television advertisement for one of its soap products. On the basis of a survey that was conducted, probabilities were assigned to the following events.The
54. An IBD/TIPP poll conducted to learn about attitudes toward investment and retirement(Investor’s Business Daily, May 5, 2000) asked male and female respondents how important they felt level of
53. Refer again to the data from the new-matriculants survey in exercise 52.a. Given that a person applied to more than one school, what is the probability that the person is 24–26 years old?b.
52. An MBA new-matriculants survey provided the following data for 2018 students.a. For a randomly selected MBA student, prepare a joint probability table for the experiment consisting of observing
51. The following crosstabulation shows household income by educational level of the head of household (Statistical Abstract of the United States: 2002).a. Develop a joint probability table.b. What
50. A telephone survey to determine viewer response to a new television show obtained the following data.
49. A study of 31,000 hospital admissions in New York State found that 4% of the admissions led to treatment-caused injuries. One-seventh of these treatment-caused injuries resulted in death, and
48. In early 2003, President Bush proposed eliminating the taxation of dividends to shareholders on the grounds that it was double taxation. Corporations pay taxes on the earnings that are later paid
47. A financial manager made two new investments—one in the oil industry and one in municipal bonds. After a one-year period, each of the investments will be classified as either successful or
46. In a BusinessWeek/Harris Poll, 1035 adults were asked about their attitudes toward business (BusinessWeek, September 11, 2000). One question asked: “How would you rate large U.S. companies on
45. In an article about investment growth, Money magazine reported that drug stocks show powerful long-term trends and offer investors unparalleled potential for strong and steady gains. The federal
44. The American Council of Education reported that 47% of college freshmen earn a degree and graduate within five years (Associated Press, May 6, 2002). Assume that graduation records show women
43. Small cars get better gas mileage, but they are not as safe as bigger cars. Small cars accounted for 18% of the vehicles on the road, but accidents involving small cars led to 11,898 fatalities
42. 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
41. 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
40. 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,
39. 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
38. A Morgan Stanley Consumer Research Survey sampled men and women and asked each whether they preferred to drink plain bottled water or a sports drink such as Gatorade or Propel Fitness water (The
37. Visa Card USA studied how frequently young consumers, ages 18 to 24, use plastic (debit and credit) cards in making purchases (Associated Press, January 16, 2006). The results of the study
36. Reggie Miller of the Indiana Pacers is the National Basketball Association’s best career free throw shooter, making 89% of his shots (USA Today, January 22, 2004). Assume that late in a
35. The U.S. Bureau of Labor Statistics collected data on the occupations of workers 25 to 64 years old. The following table shows the number of male and female workers (in millions) in each
34. The U.S. Department of Transportation reported that during November, 83.4% of Southwest Airlines flights, 75.1% of US Airways flights, and 70.1% of JetBlue flights arrived on time (USA Today,
33. In a survey of MBA students, the following data were obtained on “students’ first reason for application to the school in which they matriculated.”
32. Due to rising health insurance costs, 43 million people in the United States go without health insurance (Time, December 1, 2003). Sample data representative of the national health insurance
31. 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
30. 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?
29. 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
28. Asurvey 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
27. A 2001 preseason NCAA football poll asked respondents to answer the question, “Will the Big Ten or the Pac-10 have a team in this year’s national championship game, the Rose Bowl?” Of the
26. Data on the 30 largest stock and balanced funds provided one-year and five-year percentage returns for the period ending March 31, 2000 (The Wall Street Journal,April 10, 2000).Suppose we
25. The U.S. Census Bureau provides data on the number of young adults, ages 18–24, who are living in their parents’ home.* Let M the event a male young adult is living in his parents’ home F
24. 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
23. 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)
22. Suppose that we have a sample space with five equally likely experimental outcomes: E1, E2, E3, E4, E5. Leta. Find P(A), P(B), and P(C).b. Find P(A B). Are A and B mutually exclusive?c. Find
21. The U.S. population by age is as follows (The World Almanac, 2004). The data are in millions of people.
20. Fortune magazine publishes an annual list of the 500 largest companies in the United States.The following data show the five states with the largest number of Fortune 500 companies(The New York
19. The National Sporting Goods Association conducted a survey of persons 7 years of age or older about participation in sports activities (Statistical Abstract of the United States: 2002).The total
18. To investigate how often we eat at home as a family during the week, Harris Interactive surveyed 496 adults living with children under the age of 18 (USA Today,January 3, 2007).The survey results
17. 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
16. 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? (Hint: Use the counting
15. 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
14. 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
13. 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
12. The Powerball lottery is played twice each week in 28 states, the Virgin Islands, and the District of Columbia. To play Powerball a participant must purchase a ticket and then select five numbers
11. The National Highway Traffic Safety Administration (NHTSA) conducted a survey to learn about how drivers throughout the United States are using seat belts (Associated Press, August 25, 2003).
10. Venture capital can provide a big boost in funds available to companies. According to Venture Economics (Investor’s Business Daily, April 28, 2000), of 2374 venture capital disbursements, 1434
9. 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
8. 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
7. 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
6. 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.
5. 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
4. 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?
3. 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.
2. 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.
1. 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
70. Automobiles traveling on a road with a posted speed limit of 55 miles per hour are checked for speed by a state police radar system. Following is a frequency distribution of speeds.

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