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mathematics
statistics

Questions and Answers of Statistics

Give a scenario where the multiplicative rule applies.
Give a scenario where the partitions rule applies.
Find the numerical values ofa.b. P52c. P42d.e.f.g. P53h. P100
Determine the number of sample points contained in the sample space when you toss the following:a. 1 dieb. 2 dicec. 4 diced. n dice
Refer to the American Journal of Physical Anthropology (Vol. 142, 2010) study of the dietary habits of extinct mammals, Exercise. Recall that 18 cheek teeth extracted from skulls of an extinct
In an experiment designed to monitor impedance to leg movement, Korean engineers attached electrodes to the ankles and knees of volunteers. Of interest were the voltage readings between pairs of
Suppose you are managing 10 employees and you need to form three teams to work on different projects. Assume that each employee may serve on any team. In how many different ways can the teams be
The nine-digit Zip code has become an integral part of the U.S. postal system. a. How many different Zip codes are available for use by the postal service? (Assume that any nine-digit number can be
Gonzaga University professors conducted a study of over 1,500 television commercials and published their results in the Journal of Sociology, Social Work and Social Welfare (Vol. 2, 2008).
Mathematicians at the University of Florida solved a 30-year-old mathematics problem with the use of the theory of partitions (Explore, Fall 2000). In mathematical terminology, a partition is a
In the mid-1980s, the state of Florida ran out of combinations of letters and numbers for its license plates. Then, each license plate contained three letters of the alphabet, followed by three
A company sells midlevel models of automobiles in five different styles. A buyer can get an automobile in one of eight colors and with either standard or automatic transmission. Would it be
Intercollegiate volleyball rules require that after the opposing team has lost its serve, each of the six members of the serving team must rotate into new positions on the court. Hence, each player
Explain the difference between the two probabilities P (A | B) and P (B | A)
Suppose the events B1, B2, and B3 are mutually exclusive and complementary events such that P(B1) = .2, P(B2) = .15, and P(B3) = .65. Consider another event A such that P(A | B1) = .4, P(A | B2) =
In Molecular Systems Biology (Vol. 3, 2007), geneticists at the University of Naples (Italy) used reverse engineering to identify genes. They calculated P(G | D), where D is a gene expression data
Refer to the U.S. Army Corps of Engineers’ study on the DDT contamination of fish in the Tennessee River (in Alabama), presented in Example. Part of the investigation focused on how far upstream
Bayes’s rule was applied to the problem of HIV testing in The American Statistician (Aug. 2008). In North America, the probability of a person having HIV is .008. A test for HIV yields either a
Nondestructive evaluation (NDE) describes methods that quantitatively characterize materials, tissues, and structures by noninvasive means, such as X-ray computed tomography, ultrasonics, and
The local area network (LAN) for the College of Business computing system at a large university is temporarily shut down for repairs. Previous shutdowns have been due to hardware failure, software
Which of the following pairs of events are mutually exclusive? a. A = {The Tampa Bay Rays win the World Series next year.} B = 5Evan Longoria, Rays infielder, hits 75 home runs next year.} b. A =
A sample space consists of four sample points S1, S2, S3, and S4, where P(S1) = .2, P(S2) = .1, P(S3) = .3, and P(S4) = .4. a. Show that the sample points obey the two probability rules for a sample
The accompanying Venn diagram illustrates a sample space containing six sample points and three events, A, B, and C. The probabilities of the sample points are P(1) = .3, P(2) = .2, P(3) = .1, P(4) =
A balanced die is thrown once. If a 4 appears, a ball is drawn from urn 1; otherwise, a ball is drawn from Urn 2. Urn 1 contains four red, three white, and three black balls. Urn 2 contains six red
Find the numerical value ofa. 6!b.c.d. P62e.f. 0!g. P104h. P502
A sterile family is a couple that has no children by their deliberate choice or because they are biologically infertile. Couples who are childless by chance are not considered to be sterile.
A random sample of five students is to be selected from 50 sociology majors for participation in a special program.a. In how many different ways can the sample be drawn?b. Show how the random-number
Refer to The American Association of Nurse Anesthetists Journal (Feb. 2000) study on the use of herbal medicines before surgery, presented in Exercise. Recall that 51% of surgical patients use herbal
Beaches that exhibit high erosion rates relative to the surrounding beach are defined as erosional hot spots. The U.S. Army Corps of Engineers is conducting a study of beach hot spots. Through an
An entomologist is studying the effect of a chemical sex attractant (pheromone) on insects. Several insects are released at a site equidistant from the pheromone under study and a control substance.
In professional sports, stacking is a term used to describe the practice of African-American players being excluded from certain positions because of race. To illustrate the stacking phenomenon, the
The American Journal of Public Health (Jan. 2002) reported on a study of elderly wheelchair users who live at home. A sample of 306 wheelchair users, age 65 or older, were surveyed about whether they
Consider a lie detector called the Computerized Voice Stress Analyzer (CVSA). The manufacturer claims that the CVSA is 98% accurate and, unlike a polygraph machine, will not be thrown off by drugs
The Republican governor of a state with no income tax is appointing a committee of five members to consider changes in the income tax law. There are 15 state representatives-seven Democrats and eight
Mechanical Engineering (Feb. 2005) reported on the need for wireless networks to monitor the quality of industrial equipment. For example, consider Eaton Corp., a company that develops distribution
A clinical psychologist is given tapes of 20 subjects discussing their recent dreams. The psychologist is told that 10 are high anxiety individuals and 10 are low-anxiety individuals. The
In having children, is there a genetic factor that causes some families to favor one sex over the other? That is, does having boys or girls “run in the family”? This was the question of interest
Blackjack, a favorite game of gamblers, is played by a dealer and at least one opponent. At the outset of the game, 2 cards of a 52-card bridge deck are dealt to the player and 2 cards to the dealer.
Children who develop unexpected difficulties with the spoken language are often diagnosed as specifically language impaired (SLI). A study published in the Journal of Speech, Language, and Hearing
A version of the dice game "craps" is played in the following manner. A player starts by rolling two balanced dice. If the roll (the sum of the two numbers showing on the dice) results in a 7 or 11,
Three people play a game called "Odd Man Out." In this game, each player flips a fair coin until the outcome (heads or tails) for one of the players is not the same as that for the other two players.
In October 1994, a flaw was discovered in the Pentium microchip installed in personal computers. The chip produced an incorrect result when dividing two numbers. Intel, the manufacturer of the
Consider the discrete probability distribution shown here:a. Calculate Î¼, Ïƒ2, and Ïƒ. b. What is P(x c. Calculate Î¼ ± 2Ïƒ. d. What
According to the American Dental Association, 60% of all dentists use nitrous oxide (€œlaughing gas€) in their practice. If x equals the number of dentists in a random sample of
According to a nationwide survey, 60% of parents with young children condone spanking their child as a regular form of punishment (Tampa Tribune, Oct. 5, 2000). Consider a random sample of three
An emergency rescue vehicle is used an average of 1.3 times daily. Use the Poisson distribution to find a. The probability that the vehicle will be used exactly twice tomorrow b. The probability
A nursery advertises that it has 10 elm trees for sale. Unknown to the nursery, 3 of the trees have already been infected with Dutch elm disease and will die within a year. a. If a buyer purchases
Economists at the University of New Mexico modeled the number of casualties (deaths or missing persons) experienced by a deep-draft U.S. flag vessel over a three-year period as a Poisson random
Refer to the Applied Ecology and Environmental Research (Vol. 1, 2003) study of beech trees damaged by fungi, presented in Exercise. The researchers found that 25% of the beech trees in east central
By mistake, a manufacturer of DVD recording systems includes 3 defective systems in a shipment of 10 going out to a small retailer. The retailer has decided to accept the shipment of DVD recorders
“Hot spots” are species-rich geographical areas. A Nature (Sept. 1993) study estimated the probability of a bird species in Great Britain inhabiting a butterfly hot spot at .70. Consider a
The degree to which democratic and nondemocratic countries attempt to control the news media was examined in the Journal of Peace Research (Nov. 1997). The article reported that 80% of all democratic
In many cities, neighborhood Crime Watch groups are formed in an attempt to reduce the amount of criminal activity. Suppose one neighborhood that has experienced an average of 10 crimes per year
A “one-shot” device can be used only once; after use, the device (e.g., a nuclear weapon, space shuttle, automobile air bag) either is destroyed or must be rebuilt. The destructive nature of a
On January 28, 1986, the space shuttle Challenger exploded, killing all seven astronauts aboard. An investigation concluded that the explosion was caused by the failure of the O ring seal in the
Classify the following random variables according to whether they are discrete or continuous: a. The number of words spelled correctly by a student on a spelling test b. The amount of water flowing
Identify the following random variables as discrete or continuous: a. The amount of flu vaccine in a syringe b. The heart rate (number of beats per minute) of an American male c. The time it takes
Identify the following variables as discrete or continuous: a. The difference in reaction time to the same stimulus before and after training b. The number of violent crimes committed per month in
Consider the following probability distribution:a. List the values that x may assume. b. What value of x is most probable? c. What is the probability that x is greater than 0? d. What is the
Explain why each of the following is or is not a valid probability distribution for a discrete random variable x:a.b. c. d.
The random variable x has the discrete probability distribution shown here:a. Find P(x ‰¤ 0).b. Find P(x 7 €“ 1).c. Find P(€“1 ‰¤ x ‰¤1).d. Find P(x e. Find P(€“1 f.
Refer to the National Highway Traffic Safety Administration (NHTSA) crash tests of new car models, presented in Exercise. A summary of the driver-side star ratings for the 98 cars in the CRASH file
Entomologists are continually searching for new biological agents to control the water hyacinth, one of the world€™s worst aquatic weeds. An insect that naturally feeds on the water
According to Wired (June 2008), 35% of the world€™s solar energy cells are manufactured in China. Consider a random sample of 5 solar energy cells, and let x represent the number in the
The Ryder Cup is a three-day golf tournament played between a team of golf professionals from the United States and a team from Europe. A total of 28 matches are played between the teams; one point
Refer to the Journal of the American Law and Economics Association (Vol. 3, 2001) study of appeals of federal civil trials, presented in Exercise. A breakdown of the 678 civil cases that were
Geneticists use a grid-called a Punnett square to display all possible gene combinations in genetic crosses. (The grid is named for Reginald Punnett, a British geneticist who developed the method in
Consider the probability distribution for the random variable x shown here:a. Find µ, Ïƒ2, and s. b. Graph p(x). c. Locate Î¼ and the interval Î¼ ±
Consider the probability distribution shown here:a. Calculate Î¼, Ïƒ2, and Ïƒ. b. Graph p(x). Locate Î¼, Î¼ €“ 2Ïƒ,
Refer to Exercise, in which you found the probability distribution for x, the number of stars in a randomly selected car€™s driver-side crash rating. Find Î¼ = E(x) for this
Refer to the Annals of the Entomological Society of America (Jan. 2005) study of the number of insect eggs, x, on a blade of water hyacinth, presented in Exercise. The probability distribution for x
The chance of winning Florida’s Pick-6 Lotto game is 1 in approximately 23 million. Suppose you buy a $1 Lotto ticket in anticipation of winning the $7 million grand prize. Calculate your expected
On the popular television game show The Price is Right, contestants can play “The Showcase Showdown.” The game involves a large wheel with 20 nickel values, 5, 10, 15, 20, ..., 95, 100, marked on
Give the five characteristics of a binomial random variable.
Refer to Exercise. a. Graph the probability distribution. b. Find the mean and standard deviation of x. c. Show the mean and the two-standard-deviation interval on each side of the mean on the
Suppose x is a binomial random variable with n = 3 and p = .3.a. Calculate the value of p(x), x = 0, 1, 2, 3, using the formula for a binomial probability distribution.b. Using your answers to part
If x is a binomial random variable, use Table II in Appendix A to find the following probabilities: a. P(x = 2) for n = 10, p = .4 b. P(x ≤ 5) for n = 15, p = .6 c. P(x > 1) for n = 5, p = .1
Suppose x is a binomial random variable with n = 5 and p = .5. Compute p(x) for x = 0, 1, 2, 3, 4, and 5, using the following two methods:a. List the sample points (take S for Success and F for
According to an Associated Press/Petside.com poll, half of all pet owners would get their next dog or cat from a shelter (USA Today, May 12, 2010). Consider a random sample of 10 pet owners and
Is the bottled water you’re drinking really purified water? A study of various brands of bottled water conducted by the Natural Resources Defense Council found that 25% of bottled water is just tap
The American College of Obstetricians and Gynecologists reports that 32% of all births in the United States take place by Caesarian section each year. (National Vital Statistics Reports, Mar. 2010).
Researchers from the Educational Testing Service (ETS) found that providing immediate feedback to students answering open ended questions can dramatically improve students' future performance on
A study of gambling activity at the University Of West Georgia (UWG) discovered that 60% of the male students wagered on sports the previous year (The Sport Journal, Fall 2006). Consider a random
The United States Department of Agriculture (USDA) reports that, under its standard inspection system, one in every 100 slaughtered chickens passes inspection with fecal contamination (Tampa Tribune,
A literature professor decides to give a 20-question true–false quiz to determine who has read an assigned novel. She wants to choose the passing grade such that the probability of passing a
Chance (Fall 2001) reported that the eight men in the Rodgers family produced 24 biological children over four generations. Of these 24 children, 21 were boys and 3 were girls. How likely is it for a
Consider a Poisson random variable with probability distributionWhat is the value of λ?
Refer to Exercise 4.78.In exercisea. Graph the probability distribution. b. Find the mean and standard deviation of x.
Given that x is a random variable, for which a Poisson probability distribution provides a good approximation, use Table III in Appendix A to compute the following:a. P(x ≤ 2) when λ= 1b. P(x ≤
Suppose x is a random variable for which a Poisson probability distribution with λ = 1 provides a good characterization.a. Graph p(x) for x = 0, 1, 2, . . . , 9.b. Find μ and σ for x, and locate
As mentioned in Section 4.5, when n is large, p is small, and np ≤ 7, the Poisson probability distribution provides a good approximation to the binomial probability distribution. Since we provide
Penumbrol imaging is a technique used by nuclear engineers for imaging objects (e.g., X-rays and lasers) that emit high-energy photons. In IEICE Transactions on Information & Systems (Apr. 2005),
The Journal of Economic Psychology (Sept. 2008) published the results of a high-stakes experiment where subjects were asked how much they would pay for insuring a valuable painting. The painting was
Davy Crockett, a U.S. congressman during the 1830s, published A Narrative of the Life of David Crockett, Written by Himself. In a Chance (Spring 1999) article, researchers determined that x, the
The British Columbia Institute of Technology provides on its Web site (www.math.bcit.ca) practical applications of statistics to mechanical engineering. The following is a Poisson application. A roll
Give the characteristics of a hypergeometric distribution.
Explain the difference between sampling with replacement and sampling without replacement.
Given that x is a hypergeometric random variable with N = 8, n = 3, and r = 5, compute the following: a. P(x = 1) b. P(x = 0) c. P(x = 3) d. P(x ≥ 4)
Use the results of Exercise 4.103 to find the following probabilities:a. P(x = 1)b. P(x = 4)c. P(x ≤ 4)d. P(x ≥ 5)e. P(x < 3)f. P(x ≥ 8)
Given that x is a hypergeometric random variable with N = 10, n = 5, and r = 7:a. Display the probability distribution for x in tabular form.b. Compute the mean and variance of x.c. Graph p(x), and

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