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Statistics 13th Global Edition James T. McClave And Terry T Sincich - Solutions

Gender in two-child families. Human Biology (Feb. 2009)published a study on the gender of children in two-child families. In populations where it is just as likely to have a boy as a girl, the probabilities of having two girls, two boys, or a boy and a girl are well known. Let x represent the
Environmental vulnerability of amphibians. Many species of amphibians are declining due to dramatic changes in the environment. The environmental vulnerability of amphibian species native to Mexico was examined in Amphibian &Reptile Conservation (Aug. 2013). The researchers quantified this decline
Solar energy cells. According to the Earth Policy Institute(July 2013), 60% 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 sample that are manufactured in China. In Section 4.4, we show that the
Contaminated gun cartridges. A weapons manufacturer uses a liquid propellant to produce gun cartridges.During the manufacturing process, the propellant can get mixed with another liquid to produce a contaminated cartridge. A statistician hired by the company to investigate the level of
Choosing portable grill displays. Refer to the Journal of Consumer Research (Mar. 2003) marketing study of influencing consumer choices by offering undesirable alternatives, presented in Exercise 3.29 (p. 159). Recall that each of 124 college students selected showroom displays for portable grills.
Reliability of a manufacturing network. A team of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, Mar. 2013). An example of such a network is a system for
Medical research has shown that a certain type of chemotherapy is successful 70% of the time when used to treat skin cancer. Suppose five skin cancer patients are treated with this type of chemotherapy, and let x equal the number of successful cures out of the five. The probability distribution for
What do you mean by expectation of a discrete random variable. LO9
Will the expectation of a negative random variable be always negative? LO9
For a mound-shaped, symmetric distribution, what is the probability that x falls into the interval m { 3s? LO9
Consider the probability distribution for the random variable x shown here:x -1 1 2 5 LO9 y .2 .4 .2 .2a. Find m = E1x2.b. Find s2 = E31x - m224.c. Find s.d. Interpret the value you obtained for m.e. In this case, can the random variable x ever assume the value m? Explain.f. In general, can a
Consider the probability distribution for the random variable LO9 x shown here:x 10 15 20 25 30 35 p(x) .05 .20 .30 .25 .10 .10a. Find m, s2, and s.b. Graph p1x2.c. Locate m and the interval m { 2s on your graph. What is the probability that x will fall within the interval m { 2s?
Consider the probability distributions shown here: LO9 x 3 4 5 p(x) .3 .4 .3 y 3 4 5 p(y) .1 .8 .1a. Use your intuition to find the mean for each distribution.How did you arrive at your choice?b. Which distribution appears to be more variable? Why?c. Calculate m and s2 for each distribution.
Consider the probability distribution shown here: LO9 x -4 -3 -2 -1 0 1 2 3 4 p(x) .02 .07 .10 .15 .30 .18 .10 .06 .02a. Calculate m, s2, and s.b. Graph p1x2. Locate m, m - 2s, and m + 2s on the graph.c. What is the probability that x will fall into the interval m { 2s?
Downloading apps to your cell phone. Refer to the survey of cell phone owners, Exercise 4.27 (p. 221). There you were given the probability distribution for x, the number of apps used at least once a week by cell phone owners who have downloaded an app to their phone. LO9a. Find the mean and
Entomological Society of America (Jan. 2005) study of the number of insect eggs, x, on a blade of water hyacinth, presented in Exercise 4.28 (p. 221). The probability distribution for x is reproduced in the accompanying table. Find LO9 the mean of the probability distribution for x, and interpret
Gender in two-child families. Refer to the Human Biology(Feb. 2009) study on the gender of children in two-child families, Exercise 4.29 (p. 222). Recall that the National Health Interview Survey (NHIS) of almost 43,000 twochild families yielded the following table. You used this information in
Environmental vulnerability of amphibians. Refer to the Amphibian & Reptile Conservation (Aug. 2013) study of Environmental Vulnerability Scores (EVS) for amphibian species native to Mexico, Exercise 4.30 (p. 222). The EVS values for 382 snake species are summarized in the table below. Let x
Beach erosional hot spots. Refer to the U.S. Army Corps of Engineers’ study of beach erosional hot spots, presented in Exercise 3.167 (p. 205). The data on the nearshore bar condition for six beach hot spots are reproduced in the accompanying table. Suppose you randomly select two of these six
For the following examples, decide whether x is a binomial random variable: LO9a. A university scholarship committee must select two students to receive a scholarship for the next academic year. The committee receives 10 applications for the scholarships—6 from male students and 4 from female
The Heart Association claims that only 10% of U.S. adults over 30 years of age meet the minimum requirements established by the President’s Council on Fitness, Sports, and Nutrition. Suppose four adults are randomly selected and each is given the fitness test. LO9a. Use the steps given in Chapter
Refer to Example 4.10. Use the formula for a binomial random variable to find the probability distribution of x, where x is the number of adults who pass the fitness test. Graph the distribution. LO9
Refer to Examples 4.10 and 4.11. Calculate m and s, the mean and standard deviation, respectively, of the number of the four adults who pass the test. Interpret the results. LO9
Suppose a poll of 20 voters is taken in a large city. The purpose is to determine x, the number who favor a certain candidate for mayor. Suppose that 60% of all the city’s voters favor the candidate. LO9a. Find the mean and standard deviation of x.b. Use Table I of Appendix B to find the
Name two parameters of a binomial random variable. LO9
Give the formula for p1x2 for a binomial random variable with n = 10 and p = .3. LO9
Consider the following binomial probability distribution: LO9 p1x2 = a7 xb 1.42x1.627 - x1x = 0, 1, 2,c, 72a. How many trials (n) are in the experiment?b. What is the value of p, the probability of success?
Refer to Exercise 4.59. LO9a. 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 graph you drew in part a.
Compute the following: LO9 a.5!2!15 - 22!d. a7 7 bb. a6 2 bc. a5 0 be. a5 3 b
If x is a binomial random variable, compute p1x2 for each LO9 of the following cases:a. n = 5, x = 1, p = .2b. n = 4, x = 2, q = .4c. n = 3, x = 0, p = .7d. n = 5, x = 3, p = .1e. n = 4, x = 2, q = .6f. n = 3, x = 1, p = .9
If x is a binomial random variable, use Table I in Appendix B LO9 or technology to find the following probabilities:a. P1x = 22 for n = 10, p = .4b. P1x … 52 for n = 15, p = .6c. P1x 7 12 for n = 5, p = .1
If x is a binomial random variable, use Table I in Appendix B or technology to find the following probabilities: LO9a. P1x = 92 for n = 24, p = .7b. P1x … 52 for n = 15, p = .5c. P1x = 22 for n = 18, p = .5
If x is a binomial random variable, calculate m, s2, and s for each of the following:a. n = 8, p = .3 LO9b. n = 100, p = .2c. n = 90, p = .4d. n = 60, p = .9e. n = 50, p = .7f. n = 1,000, p = .05
Ecologists often use the number of reported sightings of a rare species of animal to estimate the remaining population size. For example, suppose the number x of reported sightings per week of blue whales is recorded. Assume that x has (approximately) a Poisson probability distribution.
What is the relation between the mean and the variance of a Poisson random variable? LO9
Consider a Poisson random variable with probability LO9 distribution p1x2 =20xe-20 x!1x = 0, 1, 2, c2 What is the value of l?
Consider the Poisson probability distribution shown here:p1x2 = LO9 5x e-5 x!1x = 0, 1, 2, c2 What is the value of l?
Refer to Exercise 4.86.a. Graph the probability distribution.b. Find the mean and standard deviation of x. LO9
Refer to Exercise 4.87.a. Graph the probability distribution. LO9b. 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, compute the following: LO9a. P1x … 12 when l = 1b. P1x … 12 when l = 2c. P1x … 12 when l = 3d. What happens to the probability of the event 5x … 16 as l increases from 1 to 3? Is
Assume that x is a random variable having a Poisson probability distribution with a mean of 2. Find the following probabilities: LO9a. P1x … 22b. P1x Ú 22c. P1x = 22d. P1x = 02e. P1x 6 12f. P1x 6 42
Suppose a professor randomly selects three new teaching assistants from a total of 10 applicants—six male and four female students. Let x be the number of females who are hired. LO9a. Find the mean and standard deviation of x.b. Find the probability that no females are hired.
Explain the difference between sampling with replacement and sampling without replacement. LO9
Give the characteristics of a hypergeometric distribution. LO9
How do binomial and hypergeometric random variables LO9 differ? In what respects are they similar?
Given that x is a hypergeometric random variable with N = 7, n = 3, and r = 4, compute the following: LO9a. P1x = 12b. P1x = 02c. P1x = 32d. P1x = 42
Given that x is a hypergeometric random variable, compute p1x2 for each of the following cases: LO9a. N = 6, n = 4, r = 4, x = 2b. N = 10, n = 6, r = 4, x = 4c. N = 3, n = 3, r = 3, x = 3d. N = 5, n = 3, r = 3, x = 1
Given that x is a hyper-geometric random variable with N = 10, n = 6, and r = 4, find the following probabilities: LO9a. P1x = 12b. P1x = 32c. P1x … 32d. P1x Ú 32e. P1x 6 22f. P1x Ú 52
Mail rooms contaminated with anthrax. In Chance (Spring 2002), research statisticians discussed the problem of sampling mail rooms for the presence of anthrax spores.Let x equal the number of mail rooms contaminated with anthrax spores in a random sample of 3 mail rooms selected from a population
Establishing boundaries in academic engineering. How academic engineers establish boundaries (e.g., differentiating between engineers and other scientists, defining the different disciplines within engineering, determining the quality of journal publications) was investigated in Engineering Studies
Identify the type of random variable—binomial, Poisson, or hypergeometric—described by each of the following LO9 probability distributions:*a. p1x2 =.5xe-.5 x!1x = 0, 1, 2, p 2b. p1x2 = a6 xb 1.22x1.826 - x 1x = 0, 1, 2, p , 62c. p1x2 =10!x!110 - x2!1.92x1.1210 - x 1x = 0, 1, 2,c, 102
Suppose x is a binomial random variable with n = 22 and p = .8.a. Find P1x = 162.b. Find P1x … 182.c. Find P1x 7 182.d. Find P112 … x … 162. LO9e. Find P115 6 x 6 202.f. Find m, s2, and s.g. What is the probability that x is in the interval m { 2s?
Given that x is a hypergeometric random variable, compute p1x2 for each of the following cases: LO9a. N = 9, n = 5, r = 4, x = 0b. N = 10, n = 6, r = 4, x = 3c. N = 6, n = 3, r = 4, x = 3
Suppose x is a binomial random variable. Find p1x2 for each of the following combinations of x, n, and p: LO9a. x = 1, n = 4, p = .2b. x = 4, n = 21, p = .4c. x = 0, n = 4, p = .5d. x = 4, n = 6, p = .6e. n = 16, x = 12, p = .8f. n = 12, x = 8, p = .7
Consider the discrete probability distribution shown here: LO9 x 5 10 12 14 p1x2 .2 .3 .1 .4a. Calculate m, s2, and s.b. What is P1x 6 122?c. Calculate m { 2s.d. What is the probability that x is in the interval m { 2s?
Suppose x is a Poisson random variable. Compute p1x2 for each of the following cases: LO9a. l = 3, x = 4b. l = 2, x = 3c. l = 1.5, x = 2
Use of laughing gas. According to the American Dental Association, 60% of all dentists use nitrous oxide (“laughing gas”) in their practice. If x equals the number of dentists LO9 in a random sample of five dentists who use laughing gas in practice, then the probability distribution of x is x 0
Benford’s Law of Numbers. Refer to the American Scientist(July–Aug. 1998) study of which integer is most likely to occur as the first significant digit in a randomly selected number LO9(Benford’s law), presented in Exercise 2.206 (p. 139).The table giving the frequency of each integer
Tracking missiles with satellite imagery. The Space-Based Infrared System (SBIRS) uses satellite imagery to detect and track missiles (Chance, Summer 2005). The probability that an intruding object (e.g., a missile) will be detected on a flight track by SBIRS is .8. Consider a sample of 20
Married-women study. According to Women’s Day magazine(Jan. 2007), 50% of married women would marry their current husbands again if given the chance. Consider the number x in a random sample of 12 married women who LO9 would marry their husbands again. Identify the discrete probability
Dutch elm disease. A nursery advertises that it has 12 elm trees for sale. Unknown to the nursery, 4 of the trees have already been infected with Dutch elm disease and will die within a year. LO9a. If a buyer purchases two trees, what is the probability that both trees will be healthy?b. Refer to
Dust mite allergies. A dust mite allergen level that exceeds 2 micrograms per gram 1mg>g2 of dust has been associated with the development of allergies. Consider a random sample of four homes, and let x be the number of homes with a dust mite level that exceeds 2 mg>g. The probability distribution
Deep-draft vessel casualties. 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 LO9 variable x. The researchers estimated E1x2 to be .03(Management Science,
Testing for spoiled wine. Suppose that you are purchasing cases of wine (10 bottles per case) and that, periodically, you select a test case to determine the adequacy of the bottles’ LO9 seals. To do this, you randomly select and test 4 bottles in the case. If a case contains 1 spoiled bottle of
Chickens with fecal contamination. The United States Department of Agriculture (USDA) reports that, under its standard inspection system, one in every 100 slaughtered chickens passes inspection for fecal contamination.In Exercise 3.21 (p. 158), you found the probability that a randomly selected
Crime Watch neighborhood. 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 8 crimes per year LO9 organizes such a group. During the first year following the creation of the
The outcomes of two variables are (Low, Medium, High)and (On, Off), respectively. An experiment is conducted in which the outcomes of each of the two variables are observed.The probabilities associated with each of the six possible outcome pairs are given in the following table:Low Medium High On
Sleep apnea and sleep stage transitioning. Sleep apnea is a common sleep disorder characterized by collapses of the upper airway during sleep. Chance (Winter 2009)investigated the role of sleep apnea in how people transition from one sleep stage to another. The various stages of sleep for a large
Attempted suicide methods. A study of attempted suicide methods was published in the journal Death Studies (Vol.38, 2014). Data for 59 suicide victims who had previously attempted suicide were collected. The table gives a breakdown of the number of suicide victims according to method used and
Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on the problem was investigated in the Jan. 2007 issue of the Journal of Behavioral Decision Making (see Exercise 1.31, p. 50). A total of 171 volunteer students participated in the experiment, where each was
Abortion provider survey. The Alan Guttmacher Institute Abortion Provider Survey is a survey of all 358 known nonhospital abortion providers in the United States (Perspectives on Sexual and Reproductive Health, Jan./Feb. 2003). For one part of the survey, the 358 providers were classified according
Fighting probability of fallow deer bucks. In Aggressive Behavior (Jan./Feb. 2007), zoologists investigated the likelihood of fallow deer bucks fighting during the mating season. During the observation period, the researchers recorded 205 encounters between two bucks. Of these, 167 involved one
Cell phone handoff behavior. A “handoff” is a term used in wireless communications to describe the process of a cell phone moving from a coverage area of one base station to another. Each base station has multiple channels(called color codes) that allow it to communicate with the cell phone.
Explain the difference between an unconditional probability and a conditional probability. LO5
Give the multiplicative rule of probability for LO5a. two independent events.b. any two events.
Give the formula for finding P1BA2. LO5
For two events, A and B, P1A2 = .4, P1B2 = .4, and P1AB2 = .75.a. Find P1A ¨ B2. LO5b. Find P1BA2.
For two events A and B, P1A2 = .4, P1B2 = .2, and P1A ¨ B2 = .1.a. Find P1AB2.b. Find P1BA2. LO5c. Are A and B independent events?
For two independent events, A and B, P1A2 = .2 and LO5 P1B2 = .6.a. Find P1A ¨ B2.b. Find P1AB2.c. Find P1A ∪ B2.
An experiment results in one of five sample points with probabilities P1E12 = .22, P1E22 = .21, P1E32 = .21, P1E42 = .24, and P1E52 = .12. The following events have been defined: LO5 A: 5E1, E36 B: 5E2, E3, E46 C: 5E1, E56a. Find P(A).b. Find P(B).c. Find P1A ¨ B2.d. Find P1AB2.e. Find P1B ¨
A box contains two white, two red, and two blue poker chips. Two chips are randomly chosen without replacement, LO5 and their colors are noted. Define the following events:A: 5Both chips are of the same color.6 B: 5Both chips are red.6 C: 5At least one chip is red or white.6 Find P1BA2, P1BAc2,
Crop damage by wild boars. Refer to the Current Zoology(Apr. 2014) study of crop damage by wild boars, Exercise 3.18(p. 158). Recall that researchers identified 157 incidents of crop damage in the study area caused by wild boars over a five-year period. The table giving the types of crops destroyed
Guilt in decision making. Refer to the Journal of Behavioral Decision Making (Jan. 2007) study of the effect of guilt emotion on how a decision maker focuses on the problem, Exercise 3.59 (p. 170). The results (number responding in each category) for the 171 study participants are reproduced in the
Sleep apnea and sleep stage transitioning. Refer to the sleep apnea study published in Chance (Winter 2009), Exercise 3.57(p. 169). Recall that the various stages of sleep for a large group of sleep apnea patients were monitored in 30-second“epochs,” and the sleep stage for the previous and
Compensatory advantage in education. According to Sociology of Education (Apr. 2014), compensatory advantage occurs when individuals from privileged backgrounds are less dependent on prior negative outcomes than individuals from disadvantaged families. The researcher applied this theory to
Fighting probability of fallow deer bucks. Refer to the Aggressive Behavior (Jan./Feb. 2007) study of fallow deer bucks fighting during the mating season, presented in Exercise 3.61 (p. 170). Recall that researchers recorded 167 encounters between two bucks, one of which clearly initiated the
A product can be shipped by four airlines, and each airline can ship via three different routes.a. How many distinct ways exist to ship the product?b. Assuming the airline and route are selected at random, what is the probability that Route 2 is used? LO5
There are 20 candidates for three different executive positions: E1, E2, and E3.How many different ways could you fill the positions? LO5
Consider the experiment discussed in Example 3.10 of tossing a coin 10 times.Show how we found that there were 210= 1,024 sample points for this experiment. LO5
Suppose there are five dangerous military missions, each requiring one soldier.In how many different ways can 5 soldiers from a squadron of 100 be assigned to these five missions? LO5
Suppose you wish to drive, in sequence, from a starting point to each of five cities, and you wish to compare the distances—and, ultimately, the costs—of the different routes. Denote the five cities as C1, C2, C3, C4, and C5.a. How many different routes would you have to compare?b. Suppose the
Suppose you are supervising four construction workers. You must assign three LO5 to job 1 and one to job 2. In how many different ways can you make this assignment?
Suppose you have 12 construction workers and you wish to assign 3 to jobsite LO5 1, 4 to jobsite 2, and 5 to jobsite 3. In how many different ways can you make this assignment?
Five soldiers from a squadron of 100 are to be chosen for a dangerous mission. LO5 In how many ways can groups of 5 be formed?
A consumer testing service is commissioned to rank the top 3 brands of laundry detergent. Ten brands are to be included in the study.a. In how many different ways can the consumer testing service arrive at the final ranking?b. If the testing service can distinguish no difference among the brands
Refer to Example 3.29. Suppose the consumer testing service is to choose the top 3 laundry detergents from the group of 10, but is not to rank them.a. In how many different ways can the testing service choose the 3 brands to be designated as top detergents?b. Assuming that the testing service makes
Give a scenario where the multiplicative rule applies. LO5
Give a scenario where the permutations rule applies. LO5
Give a scenario where the partitions rule applies. LO5
What is the difference between the permutations rule and the combinations rule? LO5

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