Introduction To Probability And Statistics 3rd Edition William Mendenhall - Solutions

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A small market orders copies of a certain magazine for its magazine rack each Suppose the store owner actually pays $2.00 for each copy of the magazine and the price to customers is $4.00. If magazines left at the end of the week have no salvage value, is it better to order three or four copies of
Refer to Exercise 12 and calculate V(Y) and sY. Then determine the probability that Y is within 1 standard deviation of its mean value.
Show that the cdf F(x) is a nondecreasing function; that is, implies that . Under what condition will ? F(x1) 5 F(x2)F(x1)
After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. At the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to
Alvie Singer lives at 0 in the accompanying diagram and has four friends who live at A, B, C, and D. One day Alvie decides to go visiting, so he tosses a fair coin twice to decide which of the four to visit. Once at a friend’s house, he will either return home or else proceed to one of the two
A consumer organization that evaluates new automobiles customarily reports the number of major defects in each car examined. Let X denote the number of major defects in a randomly selected car of a certain type. The cdf of X is as follow Calculate the following probabilities directly from the
Suppose that you read through this year’s issues of the New York Times and record each number that appears in a news article—the income of a CEO, the number of cases of wine produced by a winery, the total charitable contribution of a politician during the previous tax year, the age of a
Three couples and two single individuals have been invited to an investment seminar and have agreed to attend.Suppose the probability that any particular couple or individual arrives late is .4 (a couple will travel together in the same vehicle, so either both people will be on time or else both
A new battery’s voltage may be acceptable (A) or unacceptable (U). A certain flashlight requires two batteries, so batteries will be independently selected and tested until two acceptable ones have been found. Suppose that 90% of all batteries have acceptable voltages. Let Y denote the number of
Some parts of California are particularly earthquake-prone.Suppose that in one metropolitan area, 25% of all homeowners are insured against earthquake damage. Four homeowners are to be selected at random; let X denote the number among the four who have earthquake insurance.a. Find the probability
Many manufacturers have quality control programs that include inspection of incoming materials for defects. Suppose a computer manufacturer receives computer boards in lots of five. Two boards are selected from each lot for inspection. We can represent possible outcomes of the selection process by
A mail-order computer business has six telephone lines. Let X denote the number of lines in use at a specified time.Suppose the pmf of X is as given in the accompanying table.Calculate the probability of each of the following events.a. {at most three lines are in use}b. {fewer than three lines are
Airlines sometimes overbook flights. Suppose that for a plane with 50 seats, 55 passengers have tickets. Define the random variable Y as the number of ticketed passengers who actually show up for the flight. The probability mass function of Y appears in the accompanying tabla. What is the
The number of pumps in use at both a six-pump station and a four-pump station will be determined. Give the possible values for each of the following random variables:a. number of pumps in useb. between the numbers in use at stations 1 and 2c. number of pumps in use at either stationd. of stations
An individual named Claudius is located at the point 0 in the accompanying diagram.X 5 the total X 5 the tension Y 5 the pH Z 5 the amount X 5 the length U 5 the number Y 5 the number X 5 the number Using an appropriate randomization device (such as a tetrahedral die, one having four sides),
For each random variable defined here, describe the set of possible values for the variable, and state whether the variable is discrete.a. of unbroken eggs in a randomly chosen standard egg cartonb. of students on a class list for a particular course who are absent on the first day of classesc. of
If the sample space is an infinite set, does this necessarily imply that any rv X defined from will have an infinite set of possible values? If yes, say why. If no, give an example.
One slip will be randomly selected. Let ,, and . Show that A1 and A2 are independent, that A1 and A3 are independent, and that A2 and A3 are also independent (this is pairwise independence). However, show that, so the three events are not mutually independent.
A box contains the following four slips of paper, each having exactly the same dimensions: (1) win prize 1; (2) win prize 2; (3) win prize 3; (4) win prizes 1, 2, and
One method used to distinguish between granitic (G) and basaltic (B) rocks is to examine a portion of the infrared spectrum of the sun’s energy reflected from the rock surface. Let R1, R2, and R3 denote measured spectrum intensities at three different wavelengths; typically, for granite, whereas
Suppose that 50% of the overnight parcels are sent via express mail service E2 and the remaining 10% are sent via E3. Of those sent via E2, only 1% arrive late, whereas 5% of the parcels handled by E3 arrive late.a. What is the probability that a randomly selected parcel arrived late?b. If a
Refer to Exercise
One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air Force Base in California. Let A denote the event that the Vandenberg launch goes off on schedule, and let B represent the event that the Cape Canaveral launch goes off on
A factory uses three production lines to manufacture cans of a certain type. The accompanying table gives percentages of nonconforming cans, categorized by type of nonconforman During this period, line 1 produced 500 nonconforming cans, line 2 produced 400 such cans, and line 3 was responsible for
Suppose identical tags are placed on both the left ear and the right ear of a fox. The fox is then let loose for a period of time. Consider the two events and. Let , and assume C1 and C2 are independent events. Derive an expression (involving ) for the probability that exactly one tag is lost,
A quality control inspector is inspecting newly produced items for faults. The inspector searches an item for faults in a series of independent fixations, each of a fixed duration.Given that a flaw is actually present, let p denote the probability that the flaw is detected during any one fixation
Are these events pairwise independent (i.e., are A and B independent events, are A and C independent, and are B and C independent)? Are the three events mutually independent?
Consider independently rolling two fair dice, one red and the other green. Let A be the event that the red die shows 3 dots, B be the event that the green die shows 4 dots, and C be the event that the total number of dots showing on the two dice is
Consider the system of components connected as in the accompanying picture. Components 1 and 2 are connected in parallel, so that subsystem works iff either 1 or 2 works;since 3 and 4 are connected in series, that subsystem works iff both 3 and 4 work. If components work independently of one
If A and B are independent events, show that A and B are also independent. [Hint: First establish a relationship between , P(B), and .]
In Exercise 13, is any Ai independent of any other Aj?Answer using the multiplication property for independent events.
Show that for any three events A, B, and C with.
If , show that . [Hint: Add to both sides of the given inequality and then use the result of Exercise 56.]
For any events A and B with , show tha.
Return to the credit card scenario of Exercise 12 (Section 2.2), where , , ,, and . Calculate and interpret each of the following probabilities (a Venn diagram might help).a. b.c. d.e. Given that the selected individual has at least one card, what is the probability that he or she has a Visa
The accompanying table gives information on the type of coffee selected by someone purchasing a single cup at a particular airport kiosk.Blood Group O A B AB 1 .082 .106 .008 .004 Ethnic Group 2 .135 .141 .018 .006 3 .215 .200 .065 .020 Small Medium Large Regular 14% 20% 26%Decaf 20% 10% 10%Suppose
The population of a particular country consists of three ethnic groups. Each individual belongs to one of the four major blood groups. The accompanying joint probability table gives the proportions of individuals in the various ethnic group–blood group combinations.
Show that . Give an interpretation involving subsets.
Use Venn diagrams to verify the following two relationships for any events A and B (these are called De Morgan’s laws):a.b.[Hint: In each part, draw a diagram corresponding to the left side and another corresponding to the right side.]
The accompanying comparative boxplot of gasoline vapor coefficients for vehicles in Detroit appeared in the article“Receptor Modeling Approach to VOC Emission Inventory Validation” (J. of Envir. Engr., 1995: 483–490). Discuss any interesting features.85 12 95 105 115 Dimension Machine
Observations on burst strength (lb/in2) were obtained both for test nozzle closure welds and for production cannister nozzle welds (“Proper Procedures Are the Key to Welding Radioactive Waste Cannisters,” Welding J., Aug. 1997:61–67).Test 7200 6100 7300 7300 8000 7400 7300 7300 8000 6700 8300
0a. Determine the medians, fourths, and fourth spreads for the two samples.b. Are there any outliers in either sample? Any extreme outliers?c. Construct a comparative boxplot, and use it as a basis for comparing and contrasting the ED and non-ED samples.
Blood cocaine concentration (mg/L) was determined both for a sample of individuals who had died from cocaineinduced excited delirium (ED) and for a sample of those who had died from a cocaine overdose without excited delirium;survival time for people in both groups was at most 6 hours.The
Here is a stem-and-leaf display of the escape time data introduced in Exercise 36 of this chapter.32 55 33 49 34 35 6699 36 34469 37 03345 38 9 39 2347 40 23 41 42 4a. Determine the value of the fourth spread.b. Are there any outliers in the sample? Any extreme outliers?c. Construct a boxplot and
Grip is applied to produce normal surface forces that compress the object being gripped. Examples include two x| x n 5 5 gxi gxi 5 20,179 2 5 24,657,511 people shaking hands, or a nurse squeezing a patient’s forearm to stop bleeding. The article “Investigation of Grip Force, Normal Force,
In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessy v. Digital Equipment Corp.). The injury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable
A study of the relationship between age and various visual functions (such as acuity and depth perception) reported the fllowing observations on the area of scleral lamina (mm2)from human optic nerve heads (“Morphometry of Nerve Fiber Bundle Pores in the Optic Nerve Head of the
Exercise 34 presented the following data on endotoxin concentration in settled dust both for a sample of urban homes and for a sample of farm homes:U:3a. Determine the value of the sample standard deviation for each sample, interpret these values, and then contrast variability in the two samples.
Calculate and interpret the values of the sample median, sample mean, and sample standard deviation for the following observations on fracture strength (MPa, read from a graph in x“Heat-Resistant Active Brazing of Silicon Nitride: Mechanical Evaluation of Braze Joints,” Welding J., August,
The accompanying observations on stabilized viscosity (cP)for specimens of a certain grade of asphalt with 18% rubber added are from the article “Viscosity Characteristics of Rubber-Modified Asphalts” (J. of Materials in Civil Engr., 1996: 153–156):2781 2900 3013 2856 2888a. What are the
The value of Young’s modulus (GPa) was determined for cast plates consisting of certain intermetallic substrates, resulting in the following sample observations (“Strength and Modulus of a Molybdenum-Coated Ti-25Al-10Nb-3U1Mo Intermetallic,” J. of Materials Engr. and Performance, 1997:
An experiment to study the lifetime (in hours) for a certain type of component involved putting ten components into operation and observing them for 100 hours. Eight of the components failed during that period, and those lifetimes were recorded. Denote the lifetimes of the two components still
a. If a constant c is added to each xi in a sample, yielding, how do the sample mean and median of the yi s relate to the mean and median of the xi s? Verify your conjectures.b. If each xi is multiplied by a constantc, yielding , answer the question of part (a). Again, verify your conjectures.
A sample of automobiles was selected, and each was subjected to a 5-mph crash test. Denoting a car with no visible damage by S (for success) and a car with such damage by F, results were as follows:SSFSSSFFSSa. What is the value of the sample proportion of successes x/n?b. Replace each S with a 1
Compute the sample median, 25% trimmed mean, 10%trimmed mean, and sample mean for the lifetime data given in Exercise 27, and compare these measures.
The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104) to reach a given crack size in fastener holes intended for use in military aircraft (“Statistical Crack
Blood pressure values are often reported to the nearest 5 mmHg (100, 105, 110, etc.). Suppose the actual blood pressure values for nine randomly selected individuals are 118.6 2a. What is the median of the reported blood pressure values?b. Suppose the blood pressure of the second individual is
A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time(sec) to complete the escape (“Oxygen Consumption and Ventilation During Escape from an Offshore Platform,”Ergonomics, 1997: 281–292):389 356 359 363 375 424 325 394 402 373
The paper “Study on the Life Distribution of Microdrills”(J. of Engr. Manufacture, 2002: 301–305) reported the following observations, listed in increasing order, on drill lifetime (number of holes that a drill machines before it breaks)when holes were drilled in a certain brass alloy.11 14
The cumulative frequency and cumulative relative frequency for a particular class interval are the sum of frequencies and relative frequencies, respectively, for that interval and all intervals lying below it. If, for example, 5 5 5 5 5 5 5 IDT log10(IDT) IDT log10(IDT) IDT log10(IDT)72 Use class
A Pareto diagram is a variation of a histogram for categorical data resulting from a quality control study. Each category represents a different type of product nonconformity or production problem. The categories are ordered so that the one with the largest frequency appears on the far left, then
Consider the following data on types of health complaint(J joint swelling, F fatigue, B back pain, M muscle weakness, C coughing, N nose running/irritation, O other) made by tree planters. Obtain frequencies and relative frequencies for the various categories, and draw a histogram. (The data is
Human measurements provide a rich area of application for statistical methods. The article “A Longitudinal Study of the Development of Elementary School Children’s Private Speech” (Merrill-Palmer Q., 1990: 443–463)reported on a study of children talking to themselves (private speech). It
The accompanying data set consists of observations on shear strength (lb) of ultrasonic spot welds made on a certain type of alclad sheet. Construct a relative frequency histogram based on ten equal-width classes with boundaries 4000, 4200, . . . . [The histogram will agree with the one in
The article cited in Exercise 20 also gave the following values of the variables and:y 1010020111210011011 z 1861153004400121404 z 5 number of intersections y 5 number of cul y 11 0001 1201221102110 z 0 3 0 1 10 1 3 2 4 6 6 0 1 1 8 3 3 5 y 15030110 0 z 0 5 23 10 0 0 3a. Construct a histogram for
The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a sample of size 100, resulting in the following frequencies:Number of particles 01 2 3 4 5 6 7 Frequency 1 2 3 12 11 15 18 10 Number of particles 8 9 10 11 12 13 14
In a study of author productivity (“Lotka’s Test,” Collection Mgmt., 1982: 111–118), a large number of authors were classified according to the number of articles they had published during a certain period. The results were presented in the accompanying frequency distribution:Number of
Temperature transducers of a certain type are shipped in batches of 50.A sample of 60 batches was selected, and the number of transducers in each batch not conforming to design specifications was determined, resulting in the following data:21240132053313247023 04213113412322845131
Do running times of American movies differ somehow from running times of French movies? The author investigated this question by randomly selecting 25 recent movies of each type, resulting in the following running times:Am: 94 90 95 93 128 95 125 91 104 116 162 102 90 110 92 113 116 90 97 103 95
The accompanying specific gravity values for various wood types used in construction appeared in the article “Bolted Connection Design Values Based on European Yield Model” (J. of Structural Engr., 1993: 2169–2186):.31 .35 .36 .36 .37 .38 .40 .40 .40.41 .41 .42 .42 .42 .42 .42 .43 .44.45 .46
Every score in the following batch of exam scores is in the 60s, 70s, 80s, or 90s. A stem-and-leaf display with only the four stems 6, 7, 8, and 9 would not give a very detailed description of the distribution of scores. In such situations, it is desirable to use repeated stems. Here we could
In a famous experiment carried out in 1882, Michelson and Newcomb obtained 66 observations on the time it took for light to travel between two locations in Washington, D.C. A few of the measurements (coded in a certain manner) were and 31.a. Why are these measurements not identical?b. Is this an
4. What is the z-score for the x = 229 observed cases of cancer deaths? How do you interpret this z-score? "That's not a very large number," said Dr. Jacques Brisson of the department of social and preventive medicine at Laval University in Quebec. "It's an increase in the number of deaths related
3. Based on your estimate uu, what is the estimated standard deviation of the number of cancer death cases in both provinces? "That's not a very large number," said Dr. Jacques Brisson of the department of social and preventive medicine at Laval University in Quebec. "It's an increase in the number
2. What is a reasonable estimate of , the average number of such death cases for Ontario and Quebec? "That's not a very large number," said Dr. Jacques Brisson of the department of social and preventive medicine at Laval University in Quebec. "It's an increase in the number of deaths related to
1. Based on the above study, the 229 cancer deaths reported among women who had breast implants represents 24.5% less than the expected number among the general female population. Verify that 24.5% is the correct percentage."That's not a very large number," said Dr. Jacques Brisson of the
3. What is the z-score for the x = 58 observed cases of suicide deaths? How do you interpret this z-score in light of following comments? How safe is plastic surgery? Do breast implants reduce cancer risk? Do they increase the risk of suicide? First we consider the question: Do breast implants
2. Based on your estimate , what is the estimated standard deviation of the number of suicide cases in both provinces? How safe is plastic surgery? Do breast implants reduce cancer risk? Do they increase the risk of suicide? First we consider the question: Do breast implants increase the suicide
1. Here, the 58 reported cases represented a rate of 75% higher than is typically expected (can you verify from the above information that 75% is a correct percent- age?). What is a reasonable estimate of , the average number of such suicide cases for Ontario and Quebec?How safe is plastic surgery?
5.101 After Graduation Most of today's university graduates want to start earning money as soon as they graduate from university. However, for some decades now, the enrollment in graduate programs at Canadian universities has been increasing. About 20% of senior undergrad students are likely to
5.100 McDonald's or Burger King? Suppose that 50% of all young adults prefer McDonald's to Burger King when asked to state a preference. A group of 100 young adults were randomly selected and their preferences recorded.a. What is the probability that more than 60 preferred McDonald's?b. What is the
5.99 Engine Failure Suppose the four engines of a commercial aircraft are arranged to operate indepen- dently and that the probability of in-flight failure of a single engine is 0.01. What is the probability of these events on a given flight?a. No failures are observed.b. No more than one failure
5.98 Surgery, continued Refer to Exercise 5.97. If less than two operations were successful, how would you feel about the performance of the surgical team?
5.97 Successful Surgeries A new surgical proce- dure is said to be successful 80% of the time. Suppose the operation is performed five times and the results are assumed to be independent of one another. What are the probabilities of these events?a. All five operations are successful..b. Exactly
5.96 High Gas Prices How do you cope with the high gas prices? Do you drive less or do you have other money-wise or even environmentally friendly innovative ideas? As a result of soaring fuel prices, most Canadians are either cutting down on the amount they drive, making other significant changes
5.95 Bad Wiring Improperly wired control panels were mistakenly installed on two of eight large automated machine tools. It is uncertain which of the machine tools have the defective panels, and a sample of four tools is randomly chosen for inspection. What is the probability that the sample will
5.94 Earthquakes! Suppose that one out of every ten homeowners in the city of Kobe in western Japan has invested in earthquake insurance. If 15 homeowners are randomly chosen to be interviewed,a. What is the probability that at least one has earth- quake insurance?b. What is the probability that
5.93 Enrolling in University A west coast university has found that about 90% of its accepted applicants for enrollment in first year will actually enroll. In 2012, 1360 applicants were accepted to the university. Within what limits would you expect to find the size of the first year class at this
5.92 Stressed Out A subject is taught to do a task in two different ways. Studies have shown that when subjected to mental strain and asked to perform the task, the subject most often reverts to the method first learned, regardless of whether it was easier or more difficult. If the probability that
5.91 Safe Drivers? Evidence shows that the proba- bilty that a driver will be involved in a serious auotmo- bile accident during a given year is 0.01. A particular corporation employs 100 full-time travelling sales reps. Based on this evidence, use the Poisson approxima- tion to the binomial
5.90 Machine Breakdowns In a food process- ing and packaging plant, there are, on average, two packaging machine breakdowns per week. Assume the weekly machine breakdowns follow a Poisson distribution.a. What is the probability that there are no machine breakdowns in a given week?b. Calculate the
5.89 Poultry Problems A preliminary investigation reported that approximately 30% of locally grown poultry were infected with an intestinal parasite that, though not harmful to those consuming the poultry, decrease the usual weight growth rates in the birds. A diet supplement believed to be
5.88 Questionnaires, continued Refer to Exercise 5.87. n=20 questionnaires are sent out.a. What is the average number of questionnaires that will be returned?b. What is the standard deviation of the number of questionnaires that will be returned?c. If x 10 of the 20 questionnaires are returned to
5.87 Do You Return Your Questionnaires? The president of a company specializing in public opinion surveys claims that approximately 70% of all people to whom the agency sends questionnaires respond by filling out and returning the questionnaire. Twenty such questionnaires are sent out. Assume that
5.86 The Triangle Test A procedure often used to control the quality of name-brand food products utilizes a panel of five "tasters." Each member of the panel tastes three samples, two of which are from batches of the product known to have the desired taste and the other from the latest batch. Each
5.85 Wildlife Refuge There is significant opposi- tion among Canadians toward U.S. plans to approve drilling in the Arctic Wildlife Refuge, according to a survey commissioned by World Wildlife Fund Canada, carried out by Ekos Research Associates.17 The survey results are based on a telephone survey
5.84 Tay-Sachs Disease Tay-Sachs disease is a genetic disorder that is usually fatal in young children. If both parents are carriers of the disease, the prob- ability that their offspring will develop the disease is approximately 0.25. Suppose a husband and wife are both carriers of the disease and
5.83 Tobacco Control An Ipsos Reid poll conducted on behalf of the Canadian Cancer Society finds that the majority of British Columbians support implementing tougher tobacco control measures in the province.16 Overall, 71% of British Columbians support a ban on all smoking in workplaces and public
5.82 Defective Flash Drives A manufacturer of flash drives ships them in lots of 1200 drives per lot. Before shipment, 20 drives are randomly selected from each lot and tested. If none is defective, the lot is shipped. If one or more are defective, every drive in the lot is tested.a. What is the
5.81 Dark Chocolate Despite reports that dark chocolate is beneficial to the heart, 47% of adults still prefer milk chocolate to dark chocolate. 15 Suppose a random sample of n = 5 adults is selected and asked whether they prefer milk chocolate to dark chocolate.a. What is the probability that all

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Introduction To Probability And Statistics 3rd Edition William Mendenhall - Solutions

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