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Statistics 13th Edition James T. McClave - Solutions

Use the applet entitled Simulating the Probability of a Head with a Fair Coin to explore the relationship between the proportion of heads on several flips of a coin and the theoretical probability of getting heads on one flip of a fair coin. a. Repeat parts a-c of Applet Exercise 3.1 for the
Use the applets entitled Simulating the Probability of Rolling a 6 and Simulating the Probability of Rolling a 3 or 4 to explore the additive rule of probability. a. Explain why the applet Simulating the Probability of Rolling a 6 can also be used to simulate the probability of rolling a 3. Then
Use the applets entitled simulating the Probability of Rolling a 6 and Simulating the Probability of Rolling a 3 or 4 to simulate the probability of the complement of an event. a. Explain how the applet Simulating the Probability of Rolling a 6 can also be used to simulate the probability of the
Use the applet entitled Simulating the Probability of Rolling a 6 to simulate conditional probabilities. Begin by running the applet twice with n = 10, without resetting between runs. The data on your screen represent 20 rolls of a die. The diagram above the Roll button shows the frequency of each
Use the applet entitled Random Numbers to generate a list of 50 numbers between 1 and 100, inclusive. Use the list to find each of the following probabilities:a. The probability that a number chosen from the list is less than or equal to 50b. The probability that a number chosen from the list is
A network administrator is installing a videoconferencing module in a local area network (LAN) computer system. Of interest is the capacity of the LAN to handle users who attempt to call in for videoconferencing during peak hours. Calls are blocked if the user finds that all LAN lines are "busy."
How do binomial and hyper geometric random variables differ? In what respects are they similar?
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 of 100 mail rooms. If 20 of the 100
The Resource Conservation and Recovery Act mandates the tracking and disposal of hazardous waste produced at U.S. facilities. Professional Geographer (Feb. 2000) reported the hazardous- waste generation and disposal characteristics of 209 facilities. Only 8 of these facilities treated hazardous
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 (Aug. 2012). Participants were 10 tenured or
The Minneapolis Community Development Agency (MCDA) makes home improvement grants each year to homeowners in depressed city neighborhoods. One year, grants were awarded by the city council via a "random selection" of 140 homeowners' applications from among a total of 743 applications: 601 from the
Identify the type of random variable binomial, Poisson, or hyper geometric described by each of the following probability distributions:a. P (x) = 5xe-5 / x! (x = 0, 1, 2, ...)c. P (x) = 10! / {x! (10 - x)!} * (.9)x (.1)10-x (x = 0, 1, 2, ....10)
Suppose x is a binomial random variable with n = 20 and P = .7.a. Find P (x = 14).b. Find P (x ≤ 12).c. Find P (x > 12).d. Find P (9 ≤ x ≤ 18).e. Find P (8 < x < 18).f. Find µ, σ2, and σ.g. What is the probability that x is in the interval µ + 2σ?
Suppose x is a binomial random variable. Find p(x) for each of the following combinations of x, n, and p:a. x = 1, n = 3, p = .1b. x = 4, n = 20, p = .3c. x = 0, n = 2, p = .4d. x = 4, n = 5, p = .5e. n = 15, x = 12, p = .9f. n = 10, x = 8, p = .6
Suppose x is a Poisson random variable. Compute p(x) for each of the following cases:a. λ = 2, x = 3b. λ = 1, x = 4c. λ = .5, x = 2
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. 111). The table giving the frequency of each integer selected as the first digit in a
According to Women's Day magazine (Jan. 2007), only 50% of married women would marry their current husbands again if given the chance. Consider the number x in a random sample of 10 married women who would marry their husbands again. Identify the discrete probability distribution that best models
A dust mite allergen level that exceeds 2 micrograms per gram (Âµg/g) 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 2Âµg/g. The probability distribution for x, based on
A national poll conducted by The New York Times (May 7, 2000) revealed that 80% of Americans believe that after you die, some part of your lives on, either in a next life on earth or in heaven. Consider a random sample of 10 Americans and count x, the number who believe in life after death.a. Find
Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, presented in Exercise 3.95 (p. 157). Of the 132 bird species in the population, 38 are extinct. Suppose you randomly select 10 of the 132 bird species (without replacement)
Pediatric Exercise Science (Feb. 1995) published an article on the behavior of parents at competitive youth gymnastic meets. On the basis of a survey of the gymnasts, the researchers estimated the probability of a parent "yelling" at his or her child before, during, or after the meet as .05. In a
Refer to the Acoustical Science & Technology (Vol. 35, 2014) study of the degree to which the memorization process is impaired by irrelevant background speech (called irrelevant speech effects), Exercise 2.34 (p. 49). Recall that subjects performed a memorization task under two conditions: (1) with
The Environmental Protection Agency (EPA) limits the amount of vinyl chloride in plant air emissions to no more than 10 parts per million. Suppose the mean emission of vinyl chloride for a particular plant is 4 parts per million. Assume that the number x of parts per million of vinyl chloride in
The mean number of patients admitted per day to the emergency room of a small hospital is 2.5. If, on a given day, there are only four beds available for new patients, what is the probability that the hospital will not have enough beds to accommodate its newly admitted patients?
Give three different ways of representing the probability distribution of a discrete random variable.
How do discrete and continuous random variables differ?
Refer to the International Conference on Social Robotics (Vol. 6414, 2010) study of the trend in the design of social robots, Exercise 2.7 (p. 38). Recall that in a random sample of 106 social (or service) robots designed to entertain, educate, and care for human users, 63 were built with legs
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 number of boys in a two-child
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 using a modified Environmental
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 probability
A common transportation problem in large cities is congestion on the freeways. In the Canadian Journal of Civil Engineering (Jan. 2013), civil engineers investigated the use of variableTable for Exercise 4.30speed limits (VSL) to control the congestion problem. The study site was an urban freeway
What does the expected value of a random variable represent?
Will E (x) always be equal to a specific value of the random variable x?
For a mound-shaped, symmetric distribution, what is the probability that x falls into the interval ( ( 2s?
Consider the probability distribution for the random variable x shown here:a. Find Âµ = E(x).b. Find Ïƒ2 = E [(x - Âµ)2].c. Find Ïƒ.d. Interpret the value you obtained for Âµ.e. In this case, can the random variable x ever assume the value Âµ? Explain.f. In general, can a random
Refer to the Pew Internet & American Life Project survey of cell phone owners, Exercise 4.27 (p. 193). 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.a. Find the mean and
Refer to the Human Biology (Feb. 2009) study on the gender of children in two-child families, Exercise 4.29 (p. 194). Recall that the National Health Interview Survey (NHIS) of almost 43,000 two-child families yielded the following table. You used this information in Exercise 4.29d to find the
Refer to the Amphibian & Reptile Conservation (Aug. 2013) study of Environmental Vulnerability Scores (EVS) for amphibian species native to Mexico, Exercise 4.30 (p. 194). The EVS values for 382 snake species are summarized in the table below. Let x represent the EVS score for a randomly selected
Refer to the Journal of Systems Sciences & Systems Engineering (Mar. 2013) study of the reliability of a manufacturing system that involves multiple production lines, Exercise 4.36 (p. 195). Consider, again, the network for producing integrated circuit (IC) cards with two production lines set
Refer to the U.S. Army Corps of Engineers' study of beach erosional hot spots, presented in Exercise 3.167 (p. 177). 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 beaches and count x, the total
In the popular casino game of roulette, you can bet on whether the ball will fall in an arc on the wheel colored red, black, or green. You showed (Exercise 3.171, p. 177) that the probability of a red outcome is 18/38, that of a black outcome is 18/38, and that of a green outcome is 2/38. Suppose
Give the formula for p(x) for a binomial random variable with n = 7 and p = .2?
Consider the following binomial probability distribution:a. How many trials (n) are in the experiment? b. What is the value of p, the probability of success?
If x is a binomial random variable, use Table I in Appendix B or technology to find the following probabilities:a. P(x < 10) for n = 25, P = .7b. P (x ≥10) fir b = 15, P = .9c. P (x = 2) for n = 20, P = .2
Are Americans superstitious? A Harris (Feb. 2013) poll of over 2,000 adult Americans was designed to answer this question. One survey item concerned the phrase "see a penny, pick it up, all day long you'll have good luck." The poll found that just one-third of Americans (33%) believe finding and
Refer to the Cell (May 14, 2010) study of the ability of a mouse to recognize the odor of a potential predator, Exercise 3.63 (p. 143). Recall that the sources of these odors are typically major urinary proteins (Mups). In an experiment, 40% of lab mice cells exposed to chemically produced cat Mups
Power and Associates' North American Hotel Guest Satisfaction Index Study revealed that 66% of hotel guests are aware of the hotel's "green" conservation program. Among these guests, 72% actually participate in the program by reusing towels and bed linens. In a random sample of 15 hotel guests,
As a female, how likely are you to follow tradition and change your last name to your husband's when you get married? This was one of the questions investigated in research published in Advances in Applied Sociology (Nov. 2013). According to the study, the probability that an American female will
According to researchers at Dan Jones & Associates, 1 in every 3 women has been a victim of domestic abuse (Domestic Violence: Incidence and Prevalence Study, Sept.-Dec., 2005). This probability was obtained from a survey of 1,000 adult women residing in Utah. Suppose we randomly sample 15
A subcarrier is one telecommunication signal carrier that is piggybacked on top of another carrier so that effectively two signals are carried at the same time. Subcarriers are classified as data subcarriers (used for data transmissions), pilot subcarriers (used for channel synchronization), and
Give the four characteristics of a Poisson random variable.
Consider the Poisson probability distribution shown here: P (x) = 3xe-3 / x! (x = 0, 1, 2, .... ) What is the value of λ ?
Cognitive scientists at the University of Massachusetts designed an experiment to measure x, the number of times a reader's eye fixated on a single word before moving past that word (Memory and Cognition, Sept. 1997). For this experiment, x was found to have a mean of 1. Suppose one of the readers
The U.S. Department of Defense Reliability Analysis Center publishes Selected Topics in Assurance Related Technologies (START) sheets to help improve the quality of manufactured components and systems. One START sheet, titled "Application of the Poisson Distribution" (Vol. 9, No. 1, 2002), focuses
Use the applet entitled Random Numbers to generate a list of 25 numbers between 1 and 3, inclusive. Let x represent a number chosen from this list.a. What are the possible values of x?b. Give the probability distribution for x in table form.c. Let y be a number randomly chosen from the set 51, 2,
Run the applet entitled Simulating the Probability of a Head with a Fair Coin 10 times with n = 2, resetting between runs, to simulate flipping two coins 10 times. Count and record the number of heads each time. Let x represent the number of heads on a single flip of the coins.a. What are the
Use the applets entitled Simulating the Probability of a Head with an Unfair Coin (P(H) = 0.2) and Simulating the Probability of a Head with an Unfair Coin (P(H) = 0.8) to study the mean µ of a binomial distribution.a. Run each applet once with n = 1,000 and record the cumulative proportions. How
Open the applet entitled Sample from a Population. On the pull-down menu to the right of the top graph, select Binary. Set n = 10 as the sample size and repeatedly choose samples from the population. For each sample, record the number of 1's in the sample. Let x be the number of l's in a sample of
Use the applet entitled Simulating the Stock Market to estimate the probability that the stock market will go up each of the next two days. Repeatedly run the applet for n = 2, recording the number of ups each time. Use the proportion of 2's among your results as the estimate of the probability.
Give a characteristic of a uniform random variable.
In the Social and Natural Sciences Journal (Vol. 6, 2012), the time x (in minutes) between two successive arrivals of buses was modeled using an exponential distribution with mean ( = 3.77.a. Give the value of E(x).b. What is the standard deviation of x?c. Find P(x > 5). Interpret this
A "discrete" uniform distribution was the subject of an article published in the Journal of Probability (Vol. 2014). The random variable of interest was the number of days x in a month that a secondary school student attends a language class. Assume that x can be approximated by a uniform
Refer to the National Highway Traffic Safety Administration (NHTSA) crash test data for new cars, presented in Exercise 2.190 (p. 107). 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 while traveling at 35 miles per
Describe the shape of a normal probability distribution.
Find the area under the standard normal probability distribution between the following pairs of z-scores:a. z = 0 and z = 2.00b. z = 0 and z = 1.00c. z = 0 and z = 3d. z = 0 and z = .58e. z = -2.00 and z = 0f. z = -1.00 and z = 0g. z = -1.69 and z = 0h. z = -.58 and z = 0
Find each of the following probabilities for a standard normal random variable z:a. P (z = 1)b. P(z ≤ 1)c. P(z < 1)d. P(z > 1)e. P( -1≤ z ≤ 1)f. P( -2 ≤ z ≤ 2)g. P( -2.16 ≤ z ≤ .55)h. P( -.42 < z < 1.96)
Refer to Exercise 5.32. Find x0 such thata. 10% of the values of x are less than x0.b. 80% of the values of x are less than x0.c. 1% of the values of x are greater than x0.
Deep mixing is a ground improvement method developed for soft soils like clay, silt, and peat. Swedish civil engineers investigated the properties of soil improved by deep mixing with lime-cement columns in the journal Giorisk (Vol. 7, 2013). The mixed soil was tested by advancing a cylindrical rod
In Chance (Spring 2005), University of Denver statistician R. C. Hannum discussed casino gaming and the laws of probability. Casino games of pure chance (e.g., craps, roulette, baccarat, and keno) always yield a "house advantage." For example, in the game of double-zero roulette, the expected
Refer to the analysis of irrelevant speech effects in Exercise 2.34 (p. 49). Recall that irrelevant speech effects refer to the degree to which the memorization process is impaired by irrelevant background speech. In a study published in Acoustical Science & Technology (Vol. 35, 2014), subjects
Refer to the American Journal of Sociology (Jan. 2014) study of the characteristics of antiwar demonstrators in the United States, Exercise 2.106 (p. 77). Based on data collected for over 5,000 antiwar demonstrators over a recent 3-year period, the researchers found that the mean number of protest
Scientists at GlaxoSmithKline Medicines Research Center used high-performance liquid chromatography (HPLC) to determine the amount of drug in a tablet produced by the company (Analytical Chemistry, Dec. 15, 2009). Drug concentrations (measured as a percentage) for 50 randomly selected tablets are
Major League Baseball (MLB) has two leagues: the American League (AL), which utilizes the designated hitter (DH) to bat for the pitcher, and the National League (NL), which does not allow the DH. A player's batting average is computed by dividing the player's total number of hits by his official
Refer to The Sport Journal (Winter 2007) article on a new method for ranking the driving performance of PGA golfers, presented in Exercise 2.66 (p. 62). Recall that the method incorporates a golfer's average driving distance (yards) and driving accuracy (percentage of drives that land in the
Refer to the Geographical Analysis (Vol. 42, 2010) study of the decay properties of sandstone when exposed to the weather, Exercise 2.69 (p. 63). Recall that blocks of sandstone were cut into 300 equal-sized slices and the slices randomly divided into three groups of 100 slices each. Slices in
Refer to the data on the Aug. 2013 sanitation scores for 186 cruise ships, presented in Exercise 2.41 (p. 51). The data are saved in the SANIT file. Assess whether the sanitation scores are approximately normally distributed?
Refer to the American Journal of Physical Anthropology (Apr. 2014) study of a mutation of blond hair genotypes, Exercise 2.141 (p. 91). Recall that for each of 550 Southwest Pacific islanders, the effect of the mutation on hair pigmentation was measured with the melanin (M) index, where M ranges
For large n (say, n = 100), why is it advantageous to use the normal distribution to approximate a binomial probability?
The American Mineralogist (Oct. 2009) published a study of the evolution of uranium minerals in the Earth's crust. Researchers estimate that the trace amount of uranium x in reservoirs follows a uniform distribution ranging between 1 and 3 parts per million.a. Find E(x) and interpret its value.b.
Refer to the Psychological Science (Aug. 2011) study of fingerprint identification, Exercise 4.74 (p. 212). Recall that the study found that when presented with prints from the same individual, a novice will correctly identify the match only 75% of the time. Now consider a sample of 120 different
Open the applet entitled Sample from a Population. On the pulldown menu to the right of the top graph, select Bell shaped. The box to the left of the top graph displays the population mean, median, and standard deviation.a. Run the applet for each available value of n on the pulldown menu for the
What is the difference between a population parameter and a sample statistic?
What is a point estimator of a population parameter?
What is the difference between a biased and unbiased estimator?
How does the standard deviation of the sampling distribution of x relate to the standard deviation of the population from which the sample is selected?
State the Central Limit Theorem.
Consider the following probability distribution:a. Find Âµ, Ïƒ2 and Ïƒ.b. Find the sampling distribution of xÌ… for random samples of n = 2 measurements from this distribution by listing all possible values of xÌ…, and find the probability associated with each.c. Use the result of part
In a study on the physical activity of young adults, pediatric researchers measured overall physical activity as the total number of registered movements (counts) over a period of time and then computed the number of counts per minute (cpm) for each subject (International Journal of Obesity, Jan.
According to the American Automobile Association (AAA), the average cost of a gallon of regular unleaded fuel at gas stations in May 2014 was $3.65 (AAA Fuel Gauge Report). Assume that the standard deviation of such costs is $.15. Suppose that a random sample of n = 100 gas stations is selected
Refer to The Sport Journal (Winter 2007) analysis of critical part failures at NASCAR races, Exercise 5.106 (p. 271). Recall that researchers found that the time x (in hours) until the first critical part failure is exponentially distributed with µ = .10 and σ = .10. Now, consider a random sample
Refer to the American Journal of Sociology (Jan. 2014) study of the characteristics of antiwar demonstrators in the United States, Exercise 2.106 (p. 77). The researchers found that the mean number of protest organizations joined by antiwar demonstrators over a recent 3-year period was .90 with a
Refer to the British Medical Journal (Aug. 17, 2002) study comparing the effectiveness of hand washing with soap and hand rubbing with alcohol, presented in Exercise 2.107 (p. 78). Health care workers who used hand rubbing had a mean bacterial count of 35 per hand with a standard deviation of 59.
According to an Adweek/ Harris (July 2011) poll of U.S. adults, 35% do not work during their summer vacation. Assume that the true proportion of all U.S. adults that do not work during summer vacation is p = .35. Now consider a random sample of 500 U.S. adults.a. What is the probability that
A Harris (Feb. 2013) poll found that one-third of Americans (33%) believe finding and picking up a penny is good luck. Assume that the true proportion of all Americans who believe finding and picking up a penny is good luck is p = .33. In a random sample of 1,000 Americans, let represent the
A random sample of n = 500 observations is selected from a binomial population with p = .35.a. Give the mean and standard deviation of the (repeated) sampling distribution of , the sample proportion of successes for the 500 observations.b. Describe the shape of the sampling distribution of . Does
According to a 2012 Business Travel News survey, the average salary of a travel manager is $110,550. Assume that the standard deviation of such salaries is $30,000. Consider a random sample of 50 travel managers, and let x̅ represent the mean salary for the sample.a. What is (x̅?b. What is
According to the American Dental Association, 60% of all dentists use nitrous oxide in their practice. In a random sample of 75 dentists, let p̂ represent the proportion who use laughing gas in their practice.a. Find E(p̂).b. Find σ p̂.c. Describe the shape of the sampling distribution of
A large number of preventable errors (e.g., overdoses, botched operations, misdiagnoses) are being made by doctors and nurses in U.S. hospitals. A study of a major metropolitan hospital revealed that of every 100 medications prescribed or dispensed, 1 was in error, but only 1 in 500 resulted in an
What is the MVUE for a parameter?
How does the mean of the sampling distribution of x relate to the mean of the population from which the sample is selected?

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