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introduction to probability statistics

Questions and Answers of Introduction To Probability Statistics

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
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
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
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
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,
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
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
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
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
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
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
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.
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
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.
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,
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
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
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
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,
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
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
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
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
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
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
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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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.
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
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”
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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
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
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
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
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
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,
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
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.
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
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
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
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
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
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
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
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
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
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
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
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,
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

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