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Understandable Statistics Concepts And Methods 12th Edition Charles Henry Brase, Corrinne Pellillo Brase - Solutions

Three grades of jet fuel are blended to be used on long commercial flights. Each grade cost about the same and has about the same ignition or burn rate (gal/min) in a jet engine. The question is how to make the blend for the most consistent ignition rate. Assume the ignition rates of the three
This problem will be referred to in the study of control charts (Section 6.1). In the binomial probability distribution, let the number of trials be n = 3, and let the probability of success be p = 0.0228. Use a calculator to compute(a) The probability of two successes.(b) The probability of three
In the western United States, there are many dry-land wheat farms that depend on winter snow and spring rain to produce good crops. About 65% of the years, there is enough moisture to produce a good wheat crop, depending on the region.(a) Let r be a random variable that represents the number of
Only about 70% of all donated human blood can be used in hospitals. The remaining 30% cannot be used because of various infections in the blood. Suppose a blood bank has 10 newly donated pints of blood. Let r be a binomial random variable that represents the number of “good” pints that can be
Consider a multinomial experiment. This means the following:1. The trials are independent and repeated under identical conditions.2. The outcomes of each trial falls into exactly one of k ≥ 2 categories.3. The probability that the outcomes of a single trial will fall into ith category is pi
Aircraft inspectors (who specialize in mechanical engineering) report wing cracks in aircraft as nonexistent, detectable (but still functional), or critical (needs immediate repair). For a particular model of commercial jet 10 years old, history indicates 75% of the planes had no wing cracks, 20%
Consider a binomial distribution with n = 10 trials and the probability of success on a single trial p = 0.05.(a) Is the distribution skewed left, skewed right, or symmetric?(b) Compute the expected number of successes in 10 trials.(c) Given the low probability of success p on a single trial, would
In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet (Reference: Hawaii Data Book, Robert C. Schmitt). You work day shifts in a Honolulu hospital emergency room. At the beginning of each month you select your days off, and you pick 7 days at random
Old Friends Information Service is a California company that is in the business of finding addresses of long-lost friends. Old Friends claims to have a 70% success rate (Source: The Wall Street Journal). Suppose that you have the names of six friends for whom you have no addresses and decide to
A tidal wave or tsunami is usually the result of an earthquake in the Pacific Rim, often 1000 or more miles from Hawaii. Tsunamis are rare but dangerous. Many tsunamis are small and do little damage. However, a tsunami 9 meters or higher is very dangerous. Civil Defense authorities sound an alarm
USA Today reported that about 20% of all people in the United States are illiterate. Suppose you interview seven people at random off a city street.(a) Make a histogram showing the probability distribution of the number of illiterate people out of the seven people in the sample.(b) Find the mean
The Wall Street Journal reported that approximately 25% of the people who are told a product is improved will believe that it is, in fact, improved. The remaining 75% believe that this is just hype (the same old thing with no real improvement). Suppose a marketing study consists of a random sample
USA Today reports that about 25% of all prison parolees become repeat offenders. Alice is a social worker whose job is to counsel people on parole. Let us say success means a person does not become a repeat offender. Alice has been given a group of four parolees.(a) Find the probability P(r) of r
The probability that a single radar station will detect an enemy plane is 0.65.(a) Quota Problem How many such stations are required for 98% certainty that an enemy plane flying over will be detected by at least one station?(b) If four stations are in use, what is the expected number of stations
Have you ever tried to get out of jury duty? About 25% of those called will find an excuse (work, poor health, travel out of town, etc.) to avoid jury duty.(a) If 12 people are called for jury duty, what is the probability that all 12 will be available to serve on the jury?(b) If 12 people are
The Denver Post reported that a recent audit of Los Angeles 911 calls showed that 85% were not emergencies. Suppose the 911operators in Los Angeles have just received four calls.(a) What is the probability that all four calls are, in fact, emergencies?(b) What is the probability that three or more
The FBI Standard Survey of Crimes shows that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solved (Source: True Odds, by James Walsh, Merrit Publishing). Suppose a neighborhood district in a large city suffers repeated
A large bank vault has several automatic burglar alarms. The probability is 0.55 that a single alarm will detect a burglar.(a) How many such alarms should be used for 99% certainty that a burglar trying to enter will be detected by at least one alarm?(b) Suppose the bank installs nine alarms. What
In Japanese criminal trials, about 95% of the defendants are found guilty. In the United States, about 60% of the defendants are found guilty in criminal trials (Source: The Book of Risks, by Larry Laudan, John Wiley and Sons). Suppose you are a news reporter following seven criminal trials.(a) If
We now have the tools to solve the chapter Focus Problem. In the book A Guide to the Development and Use of the Myers–Briggs Type Indicators by Myers and McCaully, it was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with six different
The owners of a motel in Florida have noticed that in the long run, about 40% of the people who stop and inquire about a room for the night actually rent a room.(a) Quota Problem How many inquiries must the owner answer to be 99% sure of renting at least one room?(b) If 25 separate inquiries are
Let r be a binomial random variable representing the number of successes out of n trials.(a) Explain why the sample space for r consists of the set {0, 1, 2, . . . , n} and why the sum of the probabilities of all the entries in the entire sample space must be 1.(b) Explain why P(r ≥ 1) = 1 – P
Consider a binomial distribution with n = 10 trials and the probability of success on a single trial p = 0.85.(a) Is the distribution skewed left, skewed right, or symmetric?(b) Compute the expected number of successes in 10 trials.(c) Given the high probability of success p on a single trial,
Bob is a recent law school graduate who intends to take the state bar exam. According to the National Conference on Bar Examiners, about 57% of all people who take the state bar exam pass (Source: The Book of Odds by Shook and Shook, Signet). Let n = 1, 2, 3, . . . represent the number of times a
On the leeward side of the island of Oahu, in the small village of Nanakuli, about 80% of the residents are of Hawaiian ancestry (Source: The Honolulu Advertiser). Let n = 1, 2, 3, . . represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the
Approximately 3.6% of all (untreated) Jonathan apples had bitter pit in a study conducted by the botanists Ratkowsky and Martin (Source: Australian Journal of Agricultural Research, Vol. 25, pp. 783–790). (Bitter pit is a disease of apples resulting in a soggy core, which can be caused either by
At Fontaine Lake Camp on Lake Athabasca in northern Canada, history shows that about 30% of the guests catch lake trout over 20 pounds on a 4-day fishing trip (Source: Athabasca Fishing Lodges, Saskatoon, Canada). Let n be a random variable that represents the first trip to Fontaine Lake Camp
At Burnt Mesa Pueblo, in one of the archaeological excavation sites, the artifact density (number of prehistoric artifacts per 10 liters of sediment) was 1.5 (Source: Bandelier Archaeological Excavation Project: Summer 1990 Excavations at Burnt Mesa Pueblo and Casa del Rito, edited by Kohler,
In his doctoral thesis, L. A. Beckel (University of Minnesota, 1982) studied the social behavior of river otters during the mating season. An important role in the bonding process of river otters is very short periods of social grooming. After extensive observations, Dr. Beckel found that one group
The Denver Post reported that, on average, a large shopping center has had an incident of shoplifting caught by security once every 3 hours. The shopping center is open from 10A.M. to 9 P.M. (11 hours). Let r be the number of shoplifting incidents caught by security in the 11-hour period during
USA Today reported that the U.S. (annual) birthrate is about 16 per 1000 people, and the death rate is about 8 per 1000 people.(a) Explain why the Poisson probability distribution would be a good choice for the random variable r = number of births (or deaths) for a community of a given population
Henry Petroski is a professor of civil engineering at Duke University. In his book To Engineer Is Human: The Role of Failure in Successful Design, Professor Petroski says that up to 95% of all structural failures, including those of bridges, airplanes, and other commonplace products of technology,
Much of Trail Ridge Road in Rocky Mountain National Park is over 12,000 feet high. Although it is a beautiful drive in summer months, in winter the road is closed because of severe weather conditions. Winter Wind Studies in Rocky Mountain National Park by Glidden (published by Rocky Mountain Nature
USA Today reported that Parkeld, California, is dubbed the world’s earthquake capital because it sits on top of the notorious San Andreas fault. Since 1857, Parkeld has had a major earthquake on the average of once every 22 years.(a) Explain why a Poisson probability distribution would be a
Jim is a real estate agent who sells large commercial buildings. Because his commission is so large on a single sale, he does not need to sell many buildings to make a good living. History shows that Jim has a record of selling an average of eight large commercial buildings every 275 days.(a)
The Honolulu Advertiser stated that in Honolulu there was an average of 661 burglaries per 100,000 households in a given year. In the Kohola Drive neighborhood there are 316 homes. Let r = number of these homes that will be burglarized in a year.(a) Explain why the Poisson approximation to the
Harper's Index reported that the number of Orange County, California convicted drunk drivers whose sentence included a tour of the morgue was 569, of which only 1 became a repeat offender.(a) Suppose that of 1000 newly convicted drunk drivers, all were required to take a tour of the morgue. Let us
USA Today reported that for all airlines, the number of lost bags wasMay: 6.02 per 1000 passengers December: 12.78 per 1000 passengersNote: A passenger could lose more than one bag.(a) Let r = number of bags lost per 1000 passengers in May. Explain why the Poisson distribution would be a good
Risk and Odds in Everyday Life, by James Burke, reports that the probability a police officer will be killed in the line of duty is 0.5% (or less).(a) In a police precinct with 175 officers, let r = number of police officers killed in the line of duty. Explain why the Poisson approximation to
Risk and Odds in Everyday Life, by James Burke, reports that only 2% of all local franchises are business failures. A Colorado Springs shopping complex has 137 franchises (restaurants, print shops, convenience stores, hair salons, etc.).(a) Let r be the number of these franchises that are business
(a) For n = 100, p = 0.02, and r = 2, compute P(r) using the formula for the binomial distribution and your calculator:P (r) = Cn, rpr(1 – p)n–r(b) For n = 100, p = 0.02, and r = 2, estimate P(r) using the Poisson approximation to the binomial.(c) Compare the results of parts (a) and (b).
Pyramid Lake is located in Nevada on the Paiute Indian Reservation. This lake is famous for large cutthroat trout. The mean number of trout (large and small) caught from a boat is 0.667 fish per hour (Reference: Creel Chronicle, Vol. 3, No. 2).Suppose you rent a boat and go fishing for 8 hours.
In western Kansas, the summer density of hailstorms is estimated at about 2.1 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile (Reference: Agricultural Statistics, U.S. Department of Agriculture). A crop insurance company has insured a
Suppose you have binomial trials for which the probability of success on each trial is p and the probability of failure is q = 1 – p. Let k be a fixed whole number greater than or equal to 1. Let n be the number of the trial on which the kth success occurs. This means that the first k – 1
Susan is a sales representative who has a history of making a successful sale from about 80% of her sales contacts. If she makes 12 successful sales this week, Susan will get a bonus. Let n be a random variable representing the number of contacts needed for Susan to get the 12th sale.(a) Explain
Blood type A occurs in about 41% of the population (Reference: Laboratory and Diagnostic Tests by F. Fischbach). A clinic needs 3 pints of type A blood. A donor usually gives a pint of blood. Let n be a random variable representing the number of donors needed to provide 3 pints of type A blood.(a)
If you enjoy a little abstract thinking, you may want to derive the formula for the negative binomial probability distribution. Use the notation of Problem 30. Consider two events, A and B.A = {event that the first n – 1 trials contain k – 1successes}B = {event that the nth trial is a
Given a binomial experiment with n = 150 trials and probability of success on a single trial p = 0.06, find the value of l and then use the Poisson distribution to estimate the probability of r ( 2 successes?
Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of passing 77% of the students in Western Civilization each term. Let n = 1, 2, 3, . . . represent the number of times a student takes western civilization until the first
In Hawaii shark attacks are very rare. Furthermore, about 55% of all shark attacks are serious, but not fatal (Reference: Sharks of Hawaii, Dr. Leighton Taylor, University of Hawaii Press). You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical
Suppose you are a (junk) bond broker who buys only bonds that have a 50% chance of default. You want a portfolio with at least five bonds that do not default. You can dispose of the other bonds in the portfolio with no great loss. How many such bonds should you buy if you want to be 94.1% sure that
A person with a cough is a persona non grata on airplanes, elevators, or at the theater. In theaters especially, the irritation level rises with each muffled explosion. According to Dr. Brian Carlin, a Pittsburgh pulmonologist, in any large audience you’ll hear about 11 coughs per minute(a) Let r
Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in
Records over the past year show that 1 out of 350 loans made by Mammon Bank have defaulted. Find the probability that 2 or more out of 300 loans will default. Is it appropriate to use the Poisson approximation to the binomial distribution?
In Hawaii, the rate of motor vehicle theft is 551 thefts per 100,000 vehicles (Reference: U.S. Department of Justice, Federal Bureau of Investigation). A large parking structure in Honolulu has issued 482 parking permits.(a) What is the probability that none of the vehicles with a permit will
An experiment consists of tossing a coin a specified number of times and recording the outcomes.(a) What is the probability that the first head will occur on the second trial? Does this probability change if we toss the coin three times? What if we toss the coin four times? What probability
Cathy is planning to take the Certified Public Accountant Examination (CPA exam). Records kept by the college of business from which she graduated indicate that 83% of the students who graduated pass the CPA exam. Assume that the exam is changed each time it is given. Let n = 1, 2, 3, . . .
Yellowstone Park Medical Services (YPMS) provides emergency health care for park visitors. Such health care includes treatment for everything from indigestion and sunburn to more serious injuries. A recent issue of Yellowstone Today (National Park Service Publication) indicated that the average
Tri-County Bank is a small independent bank in central Wyoming. This is a rural bank that makes loans on items as small as horses and pickup trucks to items as large as ranch land. Total monthly loan requests are used by bank officials as an indicator of economic business conditions in this rural
The manager of Motel 11 has 316 rooms in Palo Alto, California. From observation over a long period of time, she knows that on an average night, 268 rooms will be rented. The long-term standard deviation is 12 rooms. This distribution is approximately mound-shaped and symmetric.(a) For 10
The visibility standard index (VSI) is a measure of Denver air pollution that is reported each day in the Denver Post. The index ranges from 0 (excellent air quality) to 200 (very bad air quality). During winter months, when air pollution is higher, the index has a mean of about 90 (rated as fair)
The Poisson distribution (Section 5.4) gives the probability for the number of occurrences for a “rare” event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let x > 0 be a
Another application for exponential distributions is supply/demand problems. The operator of a pumping station in a small Wyoming town has observed that demand for water on a typical summer afternoon is exponentially distributed with a mean of 75 cfs (cubic feet per second). Let x be a random
Consider a binomial setting in which "neutral" is defined to be a success. So, p = P(success) = P(10 ( x < 20). Suppose n = 65 geomagnetic readings are taken. Let r be a binomial random variable that represents the number of "neutral" geomagnetic readings.(a) We want to approximate the binomial
Please give a careful but brief answer to each of the following questions.(a) What is a population? How do you get a simple random sample? Give examples.(b) What is a sample statistic? What is a sampling distribution? Give examples.
Workers at a large toxic cleanup project are concerned that their white blood cell counts may have been reduced. Let x be a random variable that represents white blood cell count per cubic millimeter of whole blood in a healthy adult. Then ( ( 7500 and ( ( 1750 (Reference: Diagnostic Tests with
Write a brief but complete essay in which you describe the probability distributions you have studied so far. Which apply to discrete random variables? Which apply to continuous random variables? Under what conditions can the binomial distribution be approximated by the normal? by the Poisson?
Suppose a "hot spot" is a site with a reading of 40 or higher.(a) In a binomial setting, let us call success a "hot spot." Use Table A to find p = P(success) 5 P(40 ( x) for a single trial.(b) Suppose you decide to take readings at random until you get your first "hot spot." Let n be a random
Suppose an archaeologist is looking for geomagnetic "hot spots" in an unexplored region of Tara. As in Problem 8, we have a binomial setting where success is a "hot spot." In this case, the probability of success is p = P(40 ( x). The archaeologist takes n = 100 magnetic susceptibility readings in
Attendance at large exhibition shows in Denver averages about 8000 people per day, with standard deviation of about 500. Assume that the daily attendance figures follow a normal distribution.(a) What is the probability that the daily attendance will be fewer than 7200 people?(b) What is the
Most exhibition shows open in the morning and close in the late evening. A study of Saturday arrival times showed that the average arrival time was 3 hours and 48 minutes after the doors opened, and the standard deviation was estimated at about 52 minutes. Assume that the arrival times follow a
The amount of money spent weekly on cleaning, maintenance, and repairs at a large restaurant was observed over a long period of time to be approximately normally distributed, with mean m = $615 and standard deviation s = $42.(a) If $646 is budgeted for next week, what is the probability that the
Suppose you want to eat lunch at a popular restaurant. The restaurant does not take reservations, so there is usually a waiting time before you can be seated. Let x represent the length of time waiting to be seated. From past experience, you know that the mean waiting time is m = 18 minutes with s
Suppose an x distribution has mean ( = 5. Consider two corresponding x distributions, the first based on samples of size n = 49 and the second based on samples of size n = 81.(a) What is the value of the mean of each of the two x distributions?(b) For which x distribution is P(x̅ > 6) smaller?
Let x be a random variable that represents checkout time (time spent in the actual checkout process) in minutes in the express lane of a large grocery. Based on a consumer survey, the mean of the x distribution is about ( = 2.7 minutes, with standard deviation ( = 0.6 minute. Assume that the
The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a standard deviation of 2.5 minutes. Assume that the distribution of taxi and takeoff times is approximately normal. You may assume that the jets are lined up on a runway so that one taxies and takes
The highest dunes at Great Sand Dunes National Monument can exceed the highest dunes in the Great Sahara, extending over 700 feet in height. However, like all sand dunes, they tend to move around in the wind. This can cause a bit of trouble for temporary structures located near the “escaping”
Suppose x has a distribution with m = 72 and s – 8.(a) If random samples of size n 5 16 are selected, can we say anything about the x distribution of sample means?(b) If the original x distribution is normal, can we say anything about the x distribution of random samples of size 16? Find P(68 ≤
We have studied two approximations to the binomial, the normal approximation and the Poisson approximation (See Section 5.4). Write a brief but complete essay in which you discuss and summarize the conditions under which each approximation would be used, the formulas involved, and the assumptions
Many people consider their smart phone to be essential! Communication, news, Internet, entertainment, photos, and just keeping current are all conveniently possible with a smart phone. However, the battery better be charged or the phone is useless. Battery life of course depends on the frequency,
Hydraulic pressure in the main cylinder of the landing gear of a commercial jet is very important for a safe landing. If the pressure is not high enough, the landing gear may not lower properly. If it is too high, the connectors in the hydraulic line may spring a leak.In-flight landing tests show
The personnel office at a large electronics firm regularly schedules job interviews and maintains records of the interviews. From the past records, they have found that the length of a first interview is normally distributed, with mean μ = 35 minutes and standard deviation σ = 7 minutes.(a)
In a combined study of northern pike, cutthroat trout, rainbow trout, and lake trout, it was found that 26 out of 855 sh died when caught and released using barbless hooks on ‑ies or lures. All hooks were removed from the sh (A National Symposium on Catch and Release Fishing, Humboldt State
A random sample of 328 medical doctors showed that 171 have a solo practice (Source: Practice Patterns of General Internal Medicine, American Medical Association).(a) Let p represent the proportion of all medical doctors who have a solo practice. Find a point estimate for p.(b) Find a 95%
Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high
Please see the setting and reference in Problem 11. Independent random samples from two regions (not those cited in Problem 11) gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions.Region I: x1; n1 =
For large U.S. companies, what percentage of their total income comes from foreign sales? A random sample of technology companies (IBM, Hewlett-Packard, Intel, and others) gave the following information.Technology companies, % foreign revenue: x1; n1 = 16Another independent random sample of basic
Independent random samples of professional football and basketball players gave the following information (References: Sports Encyclopedia of Pro Football and Official NBA Basketball Encyclopedia). Note: These data are also available for download at the Companion Sites for this text. Assume that
Independent random samples of professional football and basketball players gave the following information (References: Sports Encyclopedia of Pro Football and Official NBA Basketball Encyclopedia). These data are also available for download at the Companion Sites for this text.Heights (in ft) of
The following data represent petal lengths (in cm) for independent random samples of two species of iris (Reference: E. Anderson, Bulletin American Iris Society). Note: These data are also available for download at the Companion Sites for this text.Petal length (in cm) of Iris virginica: x1; n1 =
The U.S. Geological Survey compiled historical data about Old Faithful Geyser (Yellowstone National Park) from 1870 to 1987. Some of these data are published in the book The Story of Old Faithful, by G. D. Marler (Yellowstone Association Press). Let x1 be a random variable that represents the time
“Parental Sensitivity to Infant Cues: Similarities and Differences Between Mothers and Fathers” by M. V. Graham (Journal of Pediatric Nursing, Vol. 8, No. 6) reports a study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy). Let x1 be a random
S. C. Jett is a professor of geography at the University of California, Davis. He and a colleague, V. E. Spencer, are experts on modern Navajo culture and geography. The following information is taken from their book Navajo Architecture: Forms, History, Distributions (University of Arizona Press).
“Unknown cultural affiliations and loss of identity at high elevations.” These words are used to propose the hypothesis that archaeological sites tend to lose their identity as altitude extremes are reached. This idea is based on the notion that prehistoric people tended not to take trade
David E. Brown is an expert in wildlife conservation. In his book The Wolf in the Southwest: The Making of an Endangered Species (University of Arizona Press), he lists the following weights of adult gray wolves from two regions in Old Mexico.Chihuahua region: x1 variable in poundsDurango region:
At Community Hospital, the burn center is experimenting with a new plasma compress treatment. A random sample of n1 = 316 patients with minor burns received the plasma compress treatment. Of these patients, it was found that 259 had no visible scars after treatment. Another random sample of n2 =
Female undergraduates in randomized groups of 15 took part in a self-esteem study (“There’s More to Self-Esteem than Whether It Is High or Low: The Importance of Stability of Self-Esteem,” by M. H. Kernis et al., Journal of Personality and Social Psychology, Vol. 65, No. 6). The study
What about sample size? If we want a confidence interval with maximal margin of error E and level of confidence c, then Section 7.1 shows us which formulas to apply for a single mean m and Section 7.3 shows us formulas for a single proportion p.(a) How about a difference of means? When s1 and
What about the sample size n for confidence intervals for the difference of proportions p1 – p2? Let us make the following assumptions: equal sample sizes n = n1 = n2 and all four quantities n1p1, n1q1, n2p2, and n2q2 are greater than 5. Those readers familiar with algebra can use the procedure
Given x1 and x2 distributions that are normal or approximately normal with unknown σ1 and σ2, the value of t corresponding to x̅1 – x̅2 has a distribution that is approximated by a Student’s t distribution. We use the convention that the degrees of freedom are approximately the smaller of

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