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Statistics Plus New Mylab Statistics With Pearson Etext Access Card Package 13th Edition James Mcclave ,Terry Sincich - Solutions

For a standard normal random variable, find a z-score, say, z0, such that == a. P(zzo) = .8729 b. P(zzo) = .0516 c. P(zzo) = .5 d. P(-zozzo) = .8132 e. P(zzo) = .7995 == f. P(zzo) = .004
The random variable x has a normal distribution with m = 80 and s = 20. Find the following probabilities: a. P(x85) b. P(x120) c. P(60x90) d. P(x85) e. P(x < 130) f. P(x = 95)
The random variable x has a normal distribution with m = 40 and s2= 36. Find a value of x, say, x0, such that a. P(xx) = .5 b. P(xx) = .9909 c. P(xx) = 54.16 d. P(x = x0) = .0217 e. P(xx) = .1075 f. P(xx) = .8051
Assume that x is a binomial random variable with n = 100 and p = .5. Use the normal probability distribution to approximate the following probabilities: a. P(x 48) b. P(50x65) c. P(x 70) d. P(55x58) e. P(x = 62) f. P(x 49 or x 72)
Assume that x is a random variable best described by a uniform distribution with c = 50 and d = 80.a. Find f(x).b. Find the mean and standard deviation of x.c. Graph the probability distribution for x, and locate its mean and the interval m { 2s on the graph.d. Find P1x … 602.e. Find P1x Ú
Assume that x has an exponential distribution with u = 4.Finda. P1x … 12b. P1x 7 12c. P1x = 1.42d. P1x … 62e. P12 … x … 102
NHTSA crash safety tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data for new cars, presented in Exercise 2.190(p. 135). One of the variables measured is the severity of a driver’s head injury when the car is in a head-on collision with a fixed barrier
Galaxy velocity study. Refer to the Astronomical Journal(July 1995) study of galaxy velocities, presented in Exercise 2.200(p. 137). A histogram of the velocities of 103 galaxies located in a particular cluster named A2142 is reproduced on the next page. Comment on whether the galaxy velocities are
Trajectory of an electrical circuit. Researchers have designed, built, and tested a switched-capacitor circuit for generating random signals (International Journal of Circuit Theory and Applications, May–June 1990). The circuit’s trajectory was shown to be uniformly distributed on the interval
Passing the FCAT math test. All Florida high schools require their students to demonstrate competence in mathematics by scoring 70% or above on the FCAT mathematics achievement test. The FCAT math scores of those students taking the test for the first time are normally distributed with a mean of
Improving SAT scores. Refer to the Chance (Winter 2001) study of students who paid a private tutor to help them improve their SAT scores, presented in Exercise 2.197(p. 136). The table summarizing the changes in both the SAT-Mathematics and SAT-Verbal scores for these students is reproduced here.
Alkalinity of river water. The alkalinity level of water specimens collected from the Han River in Seoul, Korea, has a mean of 50 milligrams per liter and a standard deviation of 3.2 milligrams per liter (Environmental Science & Engineering, Sept. 1, 2000). Assume that the distribution of
Weights of contaminated fish. Refer to the U.S. Army Corps of Engineers data on contaminated fish in the Tennessee River, presented in Example 1.4(p. 38). Recall that one of the variables measured for each captured fish is weight (in grams). The weights in the data set (saved in the FISHDDT file)
Melanoma deaths. According to the American Cancer Society, melanoma, a form of skin cancer, kills 15% of Americans who suffer from the disease each year. Consider a sample of 20,000 melanoma patients.a. What are the expected value and variance of x, the number of the 20,000 melanoma patients who
Where will you get your next pet? Refer to Exercise 5.86(p. 294), Recal that 50% of pet owners will get their next dog or cat from a shelter (USA Today, May 12, 2010).Now, consider a random sample of 300 pet owners, and let x be the number who will get their next dog or cat from a shelter.a. Find
Transmission delays in wireless technology. In Mobile Networks and Applications (Dec. 2003), Resource Reservation Protocol (RSVP) was applied to mobile wireless technology (e.g., a PC notebook with wireless LAN card for Internet access). A simulation study revealed that the transmission delay
Dart-throwing errors. How accurate are you at the game of darts? Researchers at Iowa State University attempted to develop a probability model for dart throws (Chance, Summer 1997). For each of 590 throws made at certain targets on a dart board, the distance from the dart to the target point was
Marine losses for an oil company. The frequency distribution shown in the accompanying table depicts the property and marine losses incurred by a large oil company over a two-year period. In the insurance business, each “loss”interval is called a layer. Research Review (Summer 1998)demonstrated
Visually impaired students. The Journal of Visual Impairment & Blindness (May–June 1997) published a study of the lifestyles of visually impaired students. Using diaries, the students kept track of several variables, including number of hours of sleep obtained in a typical day.These visually
Comparison of exam scores: red versus blue exam. Refer to the Teaching Psychology (May 1998) study of how external clues influence performance, presented in Exercise 2.128(p. 110). Recall that two different forms of a midterm psychology examination were given, one printed on blue paper and the
Waiting for an elevator. The manager of a large department store with three floors reports that the time a customer on the second floor must wait for an elevator has a uniform distribution ranging from 0 to 5 minutes. If it takes the elevator 20 seconds to go from floor to floor, find the
Length of gestation for pregnant women. On the basis of data from the National Center for Health Statistics, N. Wetzel used the normal distribution to model the length of gestation for pregnant U.S. women (Chance, Spring 2001). Gestation has a mean length of 280 days with a standard deviation of 20
Galaxy velocity study. Recall The Astronomical Journal(July 1995) study of galaxy velocity, Exercise 5.125(p. 302).The observed velocity of a galaxy located in galaxy cluster A2142 was found to have a normal distribution with a mean of 27,117 kilometers per second (km/s) and a standard deviation of
Parents who condone spanking. In Exercise 4.138(p. 254), you learned that 60% of parents with young children condone spanking their child as a regular form of punishment (Tampa Tribune, Oct. 5, 2000). A child psychologist with 200 parent clients claims that no more than 40 of the parents condone
Victims of domestic abuse. In Exercise 4.79(p. 241), you learned that some researchers believe that one in every three women has been a victim of domestic abuse (Domestic Violence: Incidence and Prevalence study, Sept.–Dec., 2005).a. For a random sample of 240 women, what is the approximate
Mile run times. A physical-fitness association is including the mile run in its secondary-school fitness test for students.The time for this event is approximately normally distributed with a mean of 470 seconds and a standard deviation of 45 seconds. If the association wants to designate the
Wear-out of used display panels. Wear-out failure time of electronic components is often assumed to have a normal distribution. Can the normal distribution be applied to the wear-out of used manufactured products, such as colored display panels? A lot of 50 used display panels was purchased by an
Fitness of cardiac patients. The physical fitness of a patient is often measured by the patient’s maximum oxygen uptake(recorded in milliliters per kilogram, ml/kg). The mean maximum oxygen uptake for cardiac patients who regularly participate in sports or exercise programs was found to be 24.1,
Forest development following wildfires. Ecological Applications (May 1995) published a study on the development of forests following wildfires in the Pacific Northwest.One variable of interest to the researcher was tree diameter at breast height 110 years after the fire.a. The population of Douglas
Sedimentary deposits in reservoirs. Geologists have successfully used statistical models to evaluate the nature of sedimentary deposits (called facies) in reservoirs. One of the models’ key parameters is the proportion P of facies bodies in a reservoir. An article in Mathematical Geology(Apr.
Normal curve approximation. A. K. Shah published a simple approximation for areas under the normal curve in The American Statistician (Feb. 1985). Shah showed that the area A under the standard normal curve between 0 and z isa. Use Shah’s approximation to find i. P10 6 z 6 1.22 ii. P10 6 z 6 2.52
Spruce budworm infestation. An infestation of a certain species of caterpillar called the spruce budworm can cause extensive damage to the timberlands of the northern United States. It is known that an outbreak of this type of infestation occurs, on the average, every 40 years.Assuming that this
Maximum time to take a test. A professor believes that if a class is allowed to work on an examination as long as desired, the times spent by the students would be approximately normal with mean 45 minutes and standard deviation 6.5 minutes. About how long should be allotted for the examination if
Dye discharged in paint. A machine used to regulate the amount of dye dispensed for mixing shades of paint can be set so that it discharges an average of m milliliters (mL)of dye per can of paint. The amount of dye discharged is known to have a normal distribution with a standard deviation of .4
Accidents at a plant. The number of serious accidents in a manufacturing plant has (approximately) a Poisson probability distribution with a mean of three serious accidents per month. It can be shown that if x, the number of events per unit time, has a Poisson distribution with mean l, then the
Water retention of soil cores. A team of soil scientists investigated the water retention properties of soil cores sampled from an uncropped field consisting of silt loam(Soil Science, Jan. 1995). At a pressure of .1 megapascal(MPa), the water content of the soil (measured in cubic meters of water
Weights of corn chip bags. The net weight per bag of a certain brand of corn chips is listed as 12 ounces. The weight of chips actually dispensed in each bag by an automated machine, when operating to specifications, is a normal random variable with mean 11.5 ounces and standard deviation .27
IQs and The Bell Curve. The controversial book, The Bell Curve (Free Press, 1994), employs statistical analyses heavily in an attempt to support the authors’ position on “intelligence and class structure in American life.”Since the book’s publication, many expert statisticians have raised
Consider the following probability distribution:a. List the values that x may assume.b. What is the probability that x is greater than 0?c. What is the probability that x = -2? x: -5 -2 p(x) .1 .2 0 1 .3 .4
Explain why each of the following is or is not a valid probability distribution for a discrete random variable x: a. x p(x) .2 02 1 .3 23 b. x -2 p(x) .25 21 -1 0 .50 .20 c. X 4 9 20 p(x) -.3 1.0 .3 32 d. x p(x) .15 2 3 5 6 .20 .40 .35
The random variable x has the following discrete probability distribution:Since the values that x can assume are mutually exclusive events, the event {x … 7} is the union of three mutually exclusive events: x: p(x:) 52 6 7 8 9 .2 .3 .2 .1 .2
The random variable x has the discrete probability distribution shown here:a. Find P1x … -12.b. Find P1x 7 -12.c. Find P1x 6 02.d. Find P1x 6 -22.e. Find P1 -4 6 x 6 -12.f. Find P1x 6 -32. x: -4 -3 -2 -1 0 p(x:) .10 .15 .40 .30 .05
NHTSA crash tests. Refer to the National Highway Traffic Safety Administration (NHTSA) crash tests of new car models, presented in Exercise 4.6(p. 216). A summary of the driver-side star ratings for the 69 cars is reproduced in the MINITAB printout in the next column.Assume that 1 of the 69 cars is
Downloading apps to your cell phone. According to a study, nearly 40% of adult cell phone owners have downloaded an application (“app”) to their cell phone. The accompanying table gives the probability distribution for x, the number of apps used at least once a week by cell phone owners who
Controlling the water hyacinth. An insect that naturally feeds on the water hyacinth, one of the world’s worst aquatic weeds, is the delphacid. Female delphacids lay anywhere from one to four eggs onto a water hyacinth blade. The Annals of the Entomological Society of America(Jan. 2005) published
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
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
Voter preferences for a committee. A “Condorcet” committee of, say, 3 members is a committee that is preferred by voters over any other committee of 3 members. A scoring function was used to determine “Condorcet” committees in Mathematical Social Sciences (Nov. 2013). Consider a committee
Punnett square for earlobes. 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 the early 1900s.) The figure on p. 224 is a Punnett square for a
Robot-sensor system configuration. Engineers at Broadcom Corp. and Simon Fraser University collaborated on research involving a robot-sensor system in an unknown environment(The International Journal of Robotics Research, Dec. 2004).As an example, the engineers presented the three-point,
Consider the probability distribution for the random variable x shown here:a. Find μ = E1x2.b. Find s2 = E31x - μ224.c. Find s.d. Interpret the value you obtained for μ.e. In this case, can the random variable x ever assume the value m? Explain.f. In general, can a random variable ever assume a
Consider the probability distribution for the random variable x shown here: x p(x) 10 15 20 25 30 35 .05 .20 .30 .25 .10 .10 960 a. Find , 2, and . b. Graph p(x). 20 c. Locate and the interval 20 on your graph. What is the probability that x will fall within the interval = 20
Consider the probability distributions shown here:a. 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. Compare these answers with your answers in parts a and
Consider the probability distribution shown here: x -4-3 -2-1 012 3 4 p(x) .02 .07 .10 .15 .30 .18 .10 .06 .02
Controlling the water hyacinth. 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 4.28(p. 221). The probability distribution for x is reproduced in the accompanying table. Find the mean
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
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
Compute the following: a. d. 5! 2!(5-2)! (7) e. 6 b. c. 53
Consider the Poisson probability distribution shown here:What is the value of λ? 5xe-5 P(x) x! (x = 0, 1, 2,...)
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
Suppose x is a binomial random variable with n = 22 and p = .8. a. Find P(x = 16). b. Find P(x 18). c. Find P(x18). d. Find P(12 x 16). e. Find P(15 < x < 20). f. Find , o, and . g. What is the probability that x is in the interval = 20
Consider the discrete probability distribution shown here: x p(x) 52 a. Calculate , 2, and . b. What is P(x < 12)? 43 10 12 14 .3 .1 .4
Suppose x is a Poisson random variable. Compute p1x2 for each of the following cases: = a. A3, x 4 b. A 2, x = 3 = c. A1.5, 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 in a random sample of five dentists who use laughing gas in practice, then the probability distribution of x isa. Find
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(Benford’s law), presented in Exercise 2.206(p. 139).The table giving the frequency of each integer selected as
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
What is the standard error of 1x1 - x22 when the samplesare large?
To use the z-statistic to test for a difference between the means of two populations, what assumptions must be made about the two samples?
Two populations are described in each of the cases that follow.In which cases would it be appropriate to apply the small-sample t-test to investigate the difference between the population means?a. Population 1: Normal distribution with variance s1 2 Population 2: Skewed to the left with variance s2
A confidence interval for 1m1 - m22 is 1 -8, 62. Which of the following inferences is correct?a. m1 7 m2b. m1 6 m2c. m1 = m2d. no significant difference between means
A confidence interval for 1m1 - m22 is 1 -12, -62. Which of the following inferences is correct?a. m1 7 m2b. m1 6 m2c. m1 = m2d. no significant difference between means
In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:a. Use a 95% confidence interval to estimate the difference between the population means 1m1 - m22.Interpret the confidence interval.b. Test
Independent random samples of 100 observations each are chosen from two normal populations with the following means and standard deviations:a. Give the mean and standard deviation of the sampling distribution of x1.b. Give the mean and standard deviation of the sampling distribution of x2.c.
Assume that s1 2 = s2 2 = s2. Calculate the pooled estimator of s2 for each of the following cases: a. Si == 180, s = 200, n = n2 = 25 b. s=25, s = 40, n = 10, n = 20 c. s = .25, s.32, n = 8, n = 12 d. s = 2300, s = 2000, n = 15, n = 18 e. Note that the pooled estimate is a weighted average of the
Independent random samples from normal populations produced the following results:a. Calculate the pooled estimate of s2.b. Do the data provide sufficient evidence to indicate that m2 7 m1? Test, using a = .10.c. Find a 90% confidence interval for 1m1 - m22.d. Which of the two inferential
Two independent random samples have been selected, 100 observations from population 1 and 100 from population 2.Sample means x1 = 60 and x2 = 40 were obtained. From previous experience with these populations, it is known that the variances are s1 2= 64 and s2 2= 100.a. Find s1x1 - x22.b. Sketch the
Independent random samples are selected from two populations and are used to test the hypothesis H0: 1m1 - m22 = 0 against the alternative Ha: 1m1 - m22 0. An analysis of 243 observations from population 1 and 323 from population 2 yielded a p-value of .125.a. Interpret the results of the test.b.
Independent random samples selected from two normal populations produced the following sample means and standard deviations:a. Assuming equal variances, conduct the test H0: 1m1 - m22 = 0 against Ha: 1m1 - m22 0 using a = .05.b. Find and interpret the 95% confidence interval for 1m1 - m22. Sample
Shared leadership in airplane crews. Human Factors(Mar. 2014) published a study that examined the effect of shared leadership by the cockpit and cabin crews of a commercial airplane. Simulated flights were taken by 84 six-person crews, where each crew consisted of a twoperson cockpit (captain and
Last name and acquisition timing. The speed with which consumers decide to purchase a product was investigated in the Journal of Consumer Research (Aug. 2011). The researchers theorized that consumers with last names that begin with letters later in the alphabet will tend to acquire items faster
Effectiveness of teaching software. The U.S. Department of Education (DOE) conducted a national study of the effectiveness of educational software. In one phase of the study, a sample of 1,516 first-grade students in classrooms that used educational software was compared to a sample of 1,103
Cognitive impairment of schizophrenics. A study of the differences in cognitive function between normal individuals and patients diagnosed with schizophrenia was published in the American Journal of Psychiatry (Apr. 2010).The total time (in minutes) a subject spent on the Trail Making Test (a
Children’s recall of TV ads. Children’s recall and recognition of television advertisements was studied in the Journal of Advertising (Spring 2006). Two groups of children were shown a 60-second commercial for Sunkist FunFruit Rock-n-Roll Shapes. One group (the A/V group) was shown the ad with
Comparing taste test rating protocols. Taste testers of new food products are presented with several competing food samples and asked to rate the taste of each on a 9-point scale(where 1 = “dislike extremely” and 9 = “like extremely”).In the Journal of Sensory Studies (June 2014), food
Bulimia study. The “fear of negative evaluation” (FNE)scores for 11 female students known to suffer from the eating disorder bulimia and 14 female students with normal eating habits, first presented in Exercise 2.44(p. 80), are reproduced in the next table. (Recall that the higher the score,
Lobster trap placement. Refer to the Bulletin of Marine Science (Apr. 2010) study of lobster trap placement, Exercise 7.41(p. 363). Recall that the variable of interest was the average distance separating traps—called trap spacing—deployed by teams of fishermen fishing for the red spiny lobster
Shopping vehicle and judgment. Refer to the Journal of Marketing Research (Dec. 2011) study of shopping cart design, Exercise 2.111(p. 106). Design engineers want to know whether you may be more likely to purchase a vice product (e.g., a candy bar) when your arm is flexed (as when carrying a
Do video game players have superior visual attention skills? Researchers at Griffin University (Australia) conducted a study to determine whether video game players have superior visual attention skills compared to non-video game players (Journal of Articles in Support of the Null Hypothesis, Vol.
Drug content assessment. Refer to Exercise 5.68(p. 287)and the Analytical Chemistry (Dec. 15, 2009) study in which scientists used high-performance liquid chromatography to determine the amount of drug in a tablet. Twenty-five tablets were produced at each of two different, independent sites. Drug
Hygiene of handshakes, high five and fist bumps. Health professionals warn that transmission of infectious diseases may occur during the traditional handshake greeting. Two alternative methods of greeting (popularized in sports) are the “high five” and the “fist bump.” Researchers compared
How do you choose to argue? In Thinking and Reasoning(Apr. 2007), researchers at Columbia University conducted a series of studies to assess the cognitive skills required for successful arguments. One study focused on whether one would choose to argue by weakening the opposing position or by
Does rudeness really matter in the workplace? A study in the Academy of Management Journal (Oct. 2007) investigated how rude behaviors influence a victim’s task performance.College students enrolled in a management course were randomly assigned to one of two experimental conditions:rudeness
Masculinity and crime. The Journal of Sociology (July 2003) published a study on the link between the level of masculinity and criminal behavior in men. Using a sample of newly incarcerated men in Nebraska, the researcher identified 1,171 violent events and 532 events in which violence was avoided
Service without a smile. Although “service with a smile”is a slogan that many businesses adhere to, there are some jobs (e.g., judges, law enforcement officers, pollsters) that require neutrality. An organization will typically provide“display rules” to guide employees on what emotions they
Ethnicity and pain perception. An investigation of ethnic differences in reports of pain perception was presented at the annual meeting of the American Psychosomatic Society (Mar. 2001). A sample of 55 blacks and 159 whites participated in the study. Subjects rated (on a 13-point scale) the
Mineral flotation in water study. Refer to the Minerals Engineering (Vol. 46–47, 2013) study of the impact of calcium and gypsum on the flotation properties of silica in water, Exercise 2.48(p. 81). Fifty solutions of deionized water were prepared both with and without calcium/gypsum, and the

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