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mathematics
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Questions and Answers of
Statistics
According to Survey of Graduate Science Engineering Students and Post doctorates, published by the U.S. National Science Foundation, the distribution of graduate science students in
Why is the basic counting rule (BCR) often referred to as the multiplication rule?
Regarding permutations and combinations, a. What is a permutation? b. What is a combination? c. What is the major distinction between the two?
Determine the value of each quantity. a. 4P3 b. 15P4 c. 6P2 d. 10P0 e. 8P8
Determine the value of each quantity. a. 7P3 b. 5P2 c. 8P4 d. 6P0 e. 9P9
A family is defined to be a group of two or more persons related by birth, marriage, or adoption and residing together in a household. According to Current Population Survey, published by the U.S.
Determine the value of each quantity.a. 7C3b. 5C2c. 8C4d. 6C0e. 9C9
How many possible samples of size 5 are possible from a population of size 70?
Refer to Example 4.27 on pages 208-209. Suppose that the developer discontinues the Shalimar model but provides an additional elevation choice, D, for each of the remaining three model choices. a.
Refer to Example 4.27 on pages 208-209. Suppose that the developer provides an additional model choice, called the Nanaimo. a. Draw a tree diagram similar to the one shown in Fig. 4.28 depicting the
The author spoke with a representative of the U.S. Postal Service and obtained the following information about zip codes. A five-digit zip code consists of five digits, of which the first three give
In the United States, telephone numbers consist of a three-digit area code followed by a seven-digit local number. Suppose neither the first digit of an area code nor the first digit of a local
Two balanced dice are rolled. Refer to Fig. 4.1 on page 159 and determine the probability that the sum of the dice isIn Figure 4.1a. 6. b. Even. c. 7 or 11. d. 2, 3, or 12.
An extrasensory perception (ESP) experiment is conducted by a psychologist. For part of the experiment, the psychologist takes 10 cards numbered 1-10 and shuffles them. Then she looks at the cards
A hand of five-card stud poker consists of an ordered arrangement of five cards from an ordinary deck of 52 playing cards. a. How many five-card stud poker hands are possible? b. How many different
The Internal Revenue Service (IRS) decides that it will audit the returns of 3 people from a group of 18. Use combination notation to express the number of possibilities and then evaluate that
At a lottery, 100 tickets were sold and three prizes are to be given. How many possible outcomes are there if a. The three prizes are equivalent? b. There is a first, second, and third prize?
Ten people attend a party. If each pair of people shakes hands, how many handshakes will occur?
Professional sports leagues commonly end their seasons with a championship series between two teams. The series ends when one team has won four games and so must last at least four games and at most
A hand of five-card draw poker consists of an unordered arrangement of five cards from an ordinary deck of 52 playing cards. a. How many five-card draw poker hands are possible? b. How many different
The U.S. Senate consists of 100 senators, 2 from each state. A committee consisting of 5 senators is to be formed. a. How many different committees are possible? b. How many are possible if no state
The Dr. Fisher's Casebook feature "Codex magistri Piscatori," appearing in an issue of Significance Magazine (Vol. 10, Issue 2, p. 28), showed an image, including the probability, of a "Venus throw,"
Suppose that you have a key ring with eight keys on it, one of which is your house key. Further suppose that you get home after dark and can't see the keys on the key ring. You randomly try one key
Refer to Example 4.36, which starts on page 214. Determine the probability that the number of defective TVs obtained by the engineer is a. Exactly one. b. At most one. c. At least one.
A biology class has 38 students. Find the probability that at least 2 students in the class have the same birthday. For simplicity, assume that there are always 365 days in a year and that birth
Mega Millions is a multi-state jackpot draw game with a jackpot starting at $15 million and growing until someone wins. In order to play, the player selects five white numbers from the numbers 1-75
A student takes a true-false test consisting of 15 questions. Assume that the student guesses at each question and find the probability that a. The student gets at least 1 question correct. b. The
From the Washington Post website, we found final results of the 2012 presidential election. According to that site, Barack Obama received about 50% of the popular vote in the battleground state of
Refer to Exercise 4.19. In E 4.19 The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for
A simple random sample of size n is to be taken without replacement from a population of size N. a. Determine the probability that any particular sample of size n is the one selected. b. Determine
Refer to Exercise 4.266, but now assume that the class consists of N students. In E 4.266 A biology class has 38 students. Find the probability that at least 2 students in the class have the same
Refer to Exercise 4.24. In Exercise 4.24 A family is defined to be a group of two or more persons related by birth, marriage, or adoption and residing together in a household. According to Current
The probability is 0.314 that the gestation period of a woman will exceed 9 months. In 4000 human gestation periods, roughly how many will exceed 9 months?
The probability is 0.667 that the favorite in a horse race will finish in the money (first, second, or third place). In 500 horse races, roughly how many times will the favorite finish in the money?
In 2013, according to the National Governors Association, 30 of the 50 state governors were Republicans. Suppose that on each day of 2013, one U.S. state governor was randomly selected to read the
The Belmont Stakes is the third leg, after the Kentucky Derby and Preakness Stakes, of the Triple Crown of thoroughbred horseracing. The morning-line betting odds of the two favorites, Orb and
Consider the set consisting of the first 12 positive whole numbers (i.e., 1-12). Determine explicitly the numbers in the set that satisfy each of the following conditions: a. At least 9 b. At most
Consider the set consisting of the first 10 positive whole numbers (i.e., 1-10). Determine explicitly the numbers in the set that satisfy each of the following conditions: a. At least 6 b. At most
Refer to Exercise 4.53. For each of the following events, list the outcomes that constitute the event and describe the event in words.In E 4.53When one die is rolled, the following six outcomes are
Refer to Exercise 4.54. For each of the following events, list the outcomes that constitute the event and describe the event in words.In E 4.54In a horse race, the odds against winning are as shown
Refer to Exercise 4.55. For each of the following events, list the outcomes that constitute the event, and describe the event in words.In E 4.55A committee consists of five executives, three women
Refer to Exercise 4.56. For each of the following events, list the outcomes that constitute the event, and describe the event in words.In E 4.56When a dime is tossed four times, there are the
The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing
Refer to Exercise 4.53.In E 4.53When one die is rolled, the following six outcomes are possible:List the outcomes constituting A = event the die comes up even, B = event the die comes up 4 or more, C
Each part of this exercise contains events from Exercise 4.54. In each case, decide whether the events are mutually exclusive.In E 4.54In a horse race, the odds against winning are as shown in the
Consider the following random experiment: First, roll a die and observe the number of dots facing up; then, toss a coin the number of times that the die shows and observe the total number of heads.
Interpret each of the following probability statements, using the frequentist interpretation of probability. a. The probability is 0.487 that a newborn baby will be a girl. b. The probability of a
According to the Congressional Directory, the official directory of the U.S. Congress, prepared by the Joint Committee on Printing, the age distribution for senators in the U.S. Congress as of Fall
The National Institute on Drug Abuse issued the report monitoring the Future, which addressed the issue of drinking, cigarette, and smokeless tobacco use for eighth, tenth, and twelfth graders.
Interpret each of the following probability statements, using the frequentist interpretation of probability. a. The probability of being dealt a pocket pair in Texas hold'em is 0.059. b. If a
From the document "Computer and Internet Use in the United States: Population Characteristics" (Current Population Survey) by T. File, we obtained the following percentage distribution of household
Refer to Exercise 4.87. Use the complementation rule to find the probability that a randomly selected U.S. senator is In E 4.87 According to the Congressional Directory, the official directory of the
Refer to Exercise 4.88. Use the complementation rule to find the probability that one of these Type 4A development corporations selected at random has receipts In E 4.88 The State of Texas maintains
The Association of American Universities published a report titled "Looking More Closely at Student Debt." This report explores the issue about the cost of a college education and its impact on
According to America's Families and Living Arrangements, published by the U.S. Census Bureau, 51.5% of U.S. adults are female, 10.4% of U.S. adults are divorced, and 6.0% of U.S. adults are divorced
Fill in the blanks. a. Data obtained by observing values of one variable of a population are called _________ data. b. Data obtained by observing values of two variables of a population are called
State the basic counting rule (BCR).
A and B are events such that P(A) = 0.2, P(B) = 0.6, and P(A& B) = 0.1. Find P(A | B) and P(B | A).
A1, A2, and A3 are mutually exclusive and exhaustive events such that P(A1) = 0.2, P(A2) = 0.5, and P(A3) = 0.3. B is an event such that P(B | A1) = 0.7, P(B | A2) = 0.8, and P(B | A3) = 0.4. a. Find
For the first four letters in the English alphabet, a. List the possible permutations of three letters from the four. b. List the possible combinations of three letters from the four. c. Use parts
The Television Bureau of Advertising publishes a report titled TV Basics for the purpose of providing information to help advertisers make the most effective and efficient use of local and national
The Internal Revenue Service compiles data on income tax returns and summarizes its findings in Statistics of Income. The first two columns of Table 4.16 show a frequency distribution (number of
Refer to Problem 30. A federal individual income tax return is selected at random. Let H = event the return shows an AGI between $20K and $100K, I = event the return shows an AGI of less than $50K, J
For the following groups of events from Problem 31, determine which are mutually exclusive. a. H and I b. I and K c. H and (not J) d. H, (not J), and K
Refer to Problems 30 and 31.In Problema. Use the second column of Table 4.16 and the f/N rule to compute the probability of each of the events H, I, J, and K. b. Express each of the events H, I, J,
Consider the events (not J), (H & I), (H or K), and (H & K) discussed in Problem 31. a. Find the probability of each of those four events, using the f/N rule and your answers from Problem 31. b.
The National Center for Education Statistics publishes information about school enrollment in the Digest of Education Statistics. Table 4.17 provides a contingency table for enrollment in public and
Refer to the information given in Problem 35. A student is selected at random.In Problema. Describe the events L3, T1, and (T1 & L3) in words. b. Find the probability of each event in part (a), and
Refer to the information given in Problem 35. A student is selected at random. a. Find P(L3 | T1) directly, using Table 4.17 and the f/N rule. Interpret the probability you obtain in terms of
Refer to the information given in Problem 35. A student is selected at random. a. Use Table 4.17 to find P(T2) and P(T2 | L2). b. Are events L2 and T2 independent? Explain your answer in terms of
During one year, the College of Public Programs at a major university awarded the following number of master's degrees. Type of degree _________________________ Frequency Master of arts
Research by B. Hatchwell et al. on divorce rates among the long-tailed tit (Aegithalos caudatus) appeared in Science News (Vol. 157, No. 20, p. 317). Tracking birds in Yorkshire from one breeding
According to M. Neitz and J. Neitz of the Medical College of Wisconsin Eye Institute, 9% of men are color blind. For four randomly selected men, determine the probability thata. None are color
The Pew Internet & American Life Project compiles data on smartphone ownership and publishes the results in the document Smartphone Ownership. The first two columns of the following table provide a
In Example 4.31 on page 211, we considered exacta wagering in horse racing. Two similar wagers are the quinella and the trifecta. In a quinella wager, the bettor picks the two horses that he or she
A bridge hand consists of an unordered arrangement of 13 cards dealt at random from an ordinary deck of 52 playing cards. a. How many possible bridge hands are there? b. Find the probability of being
According to Nielsen Media Research, 98.6% of (U.S.) households own a TV and 85.2% of TV households own a DVD player.1. Under what condition can you use the information provided to determine the
a. Obtain a relative-frequency distribution for the classification (class-level) data. b. Using your answer from part (a), determine the probability that a randomly selected UWEC undergraduate
a. The probability that you are dealt pocket aces is 1/221, or 0.00452 to three significant digits. If you studied either Sections 4.5 and 4.6 or Section 4.8, verify that probability. b. Using the
A variable x of a finite population has the following frequency distribution:Suppose a member is selected at random from the population and let X denote the value of the variable x for the member
Approximately 297 million guests visit the 400 American amusement parks annually and take 1.7 billion safe rides. The National Safety Council publishes a report titled Fixed-Site Amusement Ride
In the 1910 article "The Probability Variations in the Distribution of α Particles" (Philosophical Magazine, Series 6, No. 20, pp. 698-707), E. Rutherford and H. Geiger described the results of
M. Goodisman et al. studied patterns in queen and worker wasps and published their findings in the article "Mating and Reproduction in the Wasp Vespula germanica" (Behavioral Ecology and
In the paper "The Distribution of Wars in Time" (Journal of the Royal Statistical Society, Vol. 107, No. 3/4, pp. 242-250), L. F. Richardson analyzed the distribution of wars in time. From the data,
M. Driscoll and N. Weiss discussed the modeling and solution of problems concerning motel reservation networks in "An Application of Queuing Theory to Reservation Networks" (TIMS, Vol. 22, No. 5, pp.
At one time, a well-known restaurant chain sold cherry pies. Professor D. Lund of the University of Wisconsin - Eau Claire enlisted the help of one of his classes to gather data on the number of
According to Injury Facts, a publication of the National Safety Council, in the United States, the lifetime probability of dying in a motor-vehicle accident is 1 in 108. Use the Poisson distribution
From the U.S. Census Bureau and the article "U.S. Prison Population Falls for Third Year" by B. Montopoli of CBS News, we found that about 1 in every 200 Americans are in prison. Use this information
In a letter to the editor that appeared in the February 23, 1987, issue of U.S. News and World Report, a reader discussed the issue of space-shuttle safety. Each "criticality 1" item must have a
The second-leading genetic cause of mental retardation is Fragile X Syndrome, named for the fragile appearance of the tip of the X chromosome in affected individuals. One in 1500 males is affected
The National Aeronautics and Space Administration (NASA) compiles data on space-shuttle launches and publishes them on its website. The following table displays a frequency distribution for the
Refer to the case study on page 223. According to the experts, the odds against a PGA golfer making a hole in one are 3708 to 1; that is, the probability is 1/3709. Use the Poisson approximation to
As reported by the Associated Press, a veteran lobsterman recently hauled up a yellow lobster less than a quarter mile south of Prince Point in Harpswell Cove, Maine. Yellow lobsters are considerably
With regard to the use of a Poisson distribution to approximate binomial probabilities, on page 254 we stated that "As you might expect, the appropriate Poisson distribution is the one whose mean is
Roughly speaking, you can use the Poisson probability formula to approximate binomial probabilities when n is large and p is small (i.e., near 0). Explain how to use the Poisson probability formula
The Atlantic Hurricane Database extends back to 1851, recording among other things the number of major hurricanes striking the U.S. Atlantic and Gulf Coast per year. A major hurricane is a hurricane
When two balanced dice are rolled, 36 equally likely outcomes are possible, as depicted in Fig. 4.1 on page 159. Let Y denote the sum of the dice. a. What are the possible values of the random
The World Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919-1921 World Series, when it was a best of nine). Thus it takes at least four games and no more than
In the article "Reproductive Ecology and Cub Survival of Florida Black Bears" (Journal of Wildlife Management, Vol. 71, Issue 3, pp. 720-727), E. Garrison et al. investigated cub survival rates of
The technology consultancy Data- Genetics published the online document PIN analysis. In addition to analyzing PIN numbers, password trends were examined. Seven million all-numeric passwords were
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