New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
mathematics
statistics
Probability & Statistics For Engineers & Scientists 7th Edition Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying - Solutions
In the case of a certain type of copper wire, it is known that, on the average, 1.5 flaws occur per millimeter. Assuming that the number of flaws is a Poisson random variable, what is the probability that no flaws occur in a certain portion of wire of length 5 millimeters? What is the mean number
Potholes on a highway can be a serious problem and are in constant need of repair. With a particular type of terrain and make of concrete, past experience suggests that there are, on the average, 2 potholes per mile after a certain amount of usage. It is assumed that the Poisson process applies to
Hospital administrators in large cities anguish about problems with traffic in emergency rooms in hospitals. For a particular hospital in a large city, the staff on hand cannot accommodate the patient traffic if there are more than 10 emergency cases in a given hour. It is assumed that patient
In airport luggage screening it is known that 3% of people screened have questionable objects in their luggage. What is the probability that a string of 15 people pass through successfully before an individual is caught with a questionable object? What is the expected number in a row that passes
Computer technology has produced an environment in which "robots" operate with the use of microprocessors. The probability that a robot fails during any 6 hour shift is 0.10. What is the probability that a robot will operate at most 5 shifts before it fails?
Refusal rate in telephone polls is known to be approximately 20%. A newspaper report indicates that 50 people were interviewed before the first refusal.(a) Comment, on the validity of the report. Use a probability in your argument.(b) What is the expected number of people interviewed before a
During a manufacturing process 15 units are randomly selected each day from the production line to check the percent defective. From historical information it is known that the probability of a defective unit is 0.05. Any time that two or more defectives are found in the sample of 15, the process
An automatic welding machine is being considered for production. It will be considered for purchase if it is successful for 99% of its welds. Otherwise, it will not be considered efficient. A test is conducted on a prototype that is to perform 100 welds. The machine will be accepted for manufacture
A car rental agency at a local airport has available 5 Fords, 7 Chevrolets, 4 Dodges, 3 Hondas, and 4 Toyotas. If the agency randomly selects 9 of these cars to chauffeur delegates from the airport to the downtown convention center, find the probability that 2 Fords. 3 Chevrolets, 1 Dodge, 1 Honda,
Service calls come to a maintenance center according to a Poisson process and, on the average, 2.7 calls come per minute. Find the probability that(a) No more than 4 calls come in any minute;(b) Fewer than 2 calls come in any minute;(c) More than 10 calls come in a 5-minute period.
An electronics firm claims that the proportion of defective units of a certain process is 5%. A buyer has a standard procedure of inspecting 15 units selected randomly from a large lot. On a particular occasion, the buyer found 5 items defective.(a) What is the probability of this occurrence, given
An electronic switching device occasionally malfunctions and may need to be replaced. It is known that the device is satisfactory if it makes, on the average, no more than 0.20 error per hour. A particular 5-hour period is chosen as a "test" on the device. If no more than 1 error occurs, the device
A company generally purchases large lots of a certain kind of electronic device. A method is used that rejects a lot if two or more defective units are found in a random sample of 100 units.(a) What is the probability of rejecting a lot that is 1% defective?(b) What is the probability of accepting
A local drugstore owner knows that, on average, 100 people per hour stop by his store.(a) Find the probability that in a given 3-minutc period nobody enters the store.(b) Find the probability that in a given 3-minute period more than 5 people enter the store.
(a) Suppose that you throw 4 dice, probability that you get at least one 1. Find(b) Suppose that you throw 2 dice 24 times. Find the probability that you get at least one (1, 1), that is, you roll "snake;-eyes." [Note: The probability of part (a) is greater than the probability of part (b).]
Suppose that 500 lottery tickets are sold. Among them, 200 tickets pay off at least the cost of the ticket. Now suppose that you buy 5 tickets. Find the probability that you will win back at least the cost of 3 tickets.
Imperfections in computer circuit boards and computer chips lend themselves to statistical treatment. For a particular type of board the probability of a diode failure is 0.03. Suppose a circuit board contains 200 diodes.(a) What is the mean number of failures among the diodes?(b) What is the
The potential buyer of a particular engine requires (among other things) that the engine start successfully 10 consecutive times. Suppose the probability of a successful start is 0.990. Let us assume that the outcomes of attempted starts are independent.(a) What is the probability that the engine
The acceptance scheme for purchasing lots containing a large number of batteries is to test no more than 75 randomly selected batteries and to reject a lot if a single battery fails. Suppose the probability of a failure is 0.001.(a) What is the probability that a lot is accepted?(b) What is the
An oil drilling company ventures into various locations, and its success or failure is independent from one location to another. Suppose the probability of a success at any specific location is 0.25.(a) What is the probability that a driller drills 10 locations and finds 1 success?(b) The driller
Consider the information of Review Exercise 5.94. The driller feels that he will "hit it big" if the second success occurs on or before the sixth attempt. What is the probability that the driller will "hit it big?"
A couple decides they will continue to have children until they have two males. Assuming that P(male) = 0.5, what is the probability that their second male is their fourth child?
It is known by researchers that 1 in 100 people carry a gene that leads to the inheritance of a certain chronic disease. From a random sample of 1000 individuals, what is the probability that fewer than 7 individuals carry the gene? Use a Poisson approximation. Using the approximation, what is the
A production process produces electronic component, parts. It has presumably been established that the probability of a defective part is 0.01. During a test of this presumption, 500 items are sampled randomly and 15 defective out of the 500 were observed.(a) What is your response to the
A production process produces items in lots of 50. Sampling plans exist in which lots are pulled aside periodically and exposed to a certain type of inspection. It is usually assumed that the proportion defective in the process is very small. It is also important to the company that lots containing
Consider the situation of Review Exercise 5.99. It has been determined that the sampling plan should be extensive enough so that there is a high probability, say 0.9, that if as many as 2 defects exist in the lot of 50 being sampled, at least. 1 will be found in the sampling. With restrictions, how
Homeland Security and missile defense technology make it paramount that we be able to detect incoming projectiles or missiles. To make the defense successful, multiple radar screens are: required. Suppose it is determined that three independent screens are to be operated and the probability that,
Consider Review Exercise 5.101. Suppose if is important, that the overall system be as near perfect as possible. Assuming the: quality of the screens are: as indicated in Review Exercise 5.101,(a) How many are needed to insure that the probability that the missile gets through undetected is
Go back to Review Exercise 5.99 (a) Re-compute the probability using the binomial distribution Comment.
There are two vacancies in a certain statistics department in the United States. Five individuals apply. Two have expertise in linear models and one has expertise in applied probability. The search committee is instructed to choose the two members randomly.(a) What is the probability that the two
The manufacturer of a tricycle for children has received complaints about defective: brakes in the product. According to the design of the product and considerable: preliminary testing, it had been determined that the probability of the kind of defect in the complaint was 1 in 10000 (i.e., .0001).
Let X be a random variable with probability find the probability distribution of the random variable Y = 2 X ? 1.
Let X be a binomial random variable with probability distribution find the probability distribution of the random variable Y =X2.
Let X1 and X2 be discrete random variables with the joint multinomial distribution for x = 0, 1, 2; x2 = 0, 1, 2; x1 + x2
Let X1 and X2 be discrete random variables with joint probability distribution find the probability distribution of the random variable Y = X1X2.
Let X have the probability distribution show that the random variable Y = ?2 In A' has a chi-squared distribution with 2 degrees of freedom.
Given the random variable X with probability distribution find the probability distribution of Y = 8X3.
The speed of a molecule in a uniform gas at equilibrium is a random variable V whose probability distribution is given by where k is an appropriate constant and b depends on the absolute temperature and mass of the molecule. Find the probability distribution of the kinetic energy of the molecule W,
A dealer's profit, in units of $5000, on a new automobile is given by Y = X2, where X is a random variable having the density function(a.) Find the probability density function of the random variable Y.(b) Using the density function of Y, find the probability that the profit will be less than S500
The hospital period, in days, for patients following treatment for a certain type of kidney disorder is a random variable Y = X + 4, where X has the density function(a) Find the probability density function of the random variable Y.(b) Using the density function of Y, find the probability that the
The random variables X and Y, representing the weights of creams and toffees in 1-kilogram boxes of chocolates containing a mixture of creams, toffees, and cordials, have the joint density function(a) Find the probability density function of the random variable Z = X + Y.(b) Using the density
The amount of kerosene, in thousands of liters, in a tank at the beginning of any day is a random amount Y from which a random amount X is sold during that day. Assume that the joint density function of these variables is given by find the probability density function for the amount of kerosene
Let X1 and X2 be independent random variables each having the probability distribution show that the random variables Y1 and Y2 are independent when Y1 = X1 + X2 and Y2 ? X1(X +X2).
A current of I amperes flowing through a resistance of R ohms varies according to the probability distribution if the resistance varies independently of the current according to the probability distribution find the probability distribution for the power W = I2Rwatts.
Let X be a random variable with probability distribution find the probability distribution of the random variable Y = X2.
Let X have the probability distribution Find the probability distribution of the random variable Y =X2.
Show that the rth moment about the origin of the gamma distribution is
A random variable X has the discrete uniform distribution show that the moment-generating function of Xis
A random variable X has the geometric distribution g(x; p) = pqx?1 for x = 1, 2, 3 Show that the moment-generating function of X is and then use Mx(t) to find the mean and variance of the geometric distribution.
A random variable X has the Poisson distribution p(x; ?) = e?? ??/x for x = 0, 1, 2, Show that the moment-generating function of X is using Mx(t), find the mean and variance of the Poisson distribution.
The moment-generating function of a certain Poisson random variable X is given by find P(p – 2σ
Using the moment-generating function of Example 7.8, show that the mean and variance of the chi-squared distribution with v degrees of freedom are, respectively, v and 2v
Dy expanding et? in a Maclaurin series and integrating term by term, show that
If both A' and Y, distributed independently, follow exponential distributions with mean parameter 1. Find the distributions of(a) U = X + Y, and(b) V = X/(X + Y).
Show that the mean square error s2 = SSE/ k (n - l) for the analysis of variance in a one-way classification is an unbiased estimate of a2.
Prove Theorem.
Six different machines are being considered for use in manufacturing rubber seals. The machines are being compared with respect, to tensile strength of the product. A random sample of 4 seals from each machine is used to determine whether the mean tensile strength varies from machine to machine.
The data in the following table represent the number of hours of relief provided by 5 different brands of headache tablets administered to 25 subjects experiencing fevers of 38?C or more. Perform the: analysis of variance and test the hypothesis at the 0.05 level of significance that, the mean
In an article Shelf-Space Strategy in Retailing, published in the Proceedings: Southern Marketing Association, the effect of shelf height on the supermarket sales of canned dog food is investigated. An experiment was conducted at a small supermarket for a period of 8 days on the sales of a single
Immobilization of free-ranging white-tailed deer by drugs allows researchers the opportunity to closely examine deer and gather valuable physiological information. In the study Influence of Physical Restraint and Restraint Facilitating Drugs on Blood Measurements of White-Tailed Deer and Other
It has been shown that the fertilizer magnesium ammonium phosphate, MgNH4PO4, is an effective supplier of the nutrients necessary for plant growth. The compounds supplied by this fertilizer are highly soluble in water, allowing the fertilizer to be applied directly on the soil surface or mixed with
A study measures the sorption (either absorption or adsorption) rate of three different types of organic chemical solvents. These solvents are used to clean industrial fabricated-metal parts and are potential hazardous waste. Independent samples of solvents from each type were tested and their
The mitochondrial enzyme NAPH: NAD transhydrogenase of the common rat tapeworm (Hymenolepiasis diminuta) catalyzes hydrogen in transfer from NADYH to NAD, producing NADH. This enzyme is known to serve a vital role in the tapeworm's anaerobic metabolism, and it has recently been hypothesized that it
For the data set in Exercise 13.7, use Bartlett's test to check whether the variances are equal.
Consider the data of Review Exercise 13.58. Make significance tests on the following contrasts:(a) B versus A, C, and D;(b) C versus A and D;(c) A versus D.
The study Loss of Nitrogen through Sweat by Preadolescent Boys Consuming Three Levels of Dietary Protein was conducted by the Department of Human Nutrition and Foods at the Virginia Polytechnic Institute and State University to determine perspiration nitrogen loss at, various dietary protein
The purpose of the study The Incorporation of a. Chelating Agent into a Flame Retardant Finish of a Cotton Flannelette and the Evaluation of Selected Fabric Properties conducted at the Virginia Polytechnic Institute and State University was to evaluate: the use of a chelating agent as part of the
Use Tukey’s test, with a 0.05 level of significance, to analyze the means of the 5 different brands of headache tablets in Exercise 13.4.
For the data used in Review Exercise 13.58, perform Tukey's test with a 0.05 level of significance to determine which laboratories differ, on average, in their analysis.
An investigation was conducted to determine the source of reduction in yield of a certain chemical product. It was known that the loss in yield occurred in the mother liquor, that is. The material removed at the filtration stage. It was felt that different blends of the original material may result
In the study An Evaluation of the Removal Method for Estimating Benthic Populations and Diversity conducted by the Virginia Polytechnic Institute and State University on the Jackson River, 5 different sampling procedures were used to determine the species count. Twenty samples were selected at
The following data are values of pressure (psi) in a torsion spring for several settings of the angle between the legs of the spring in a free position. Compute a one-way analysis of variance for this experiment and state your conclusion concerning the effect of angle on the pressure in the spring.
In the following biological experiment 4 concentrations of a certain chemical are used to enhance the growth of a certain type of plant over time. Five plants are used at each concentration and the growth in each plant is measured in centimeters. The following growth data are taken. A control (no
The following table (A. Held Statistical theory with Engineering Applications John Wiley fc Sons New York. 1952) gives tensile1 st lengths of deviations from 340 for wires taken from nine cables to be used for a high-voltage network. Each cable is made from 12 wires. We want to know whether the
The financial structure of a firm refers to the way the firm's assets are divided by equity and debt, and the financial leverage refers to the percentage of assets financed by debt. In the paper The Effect of Financial Leverage on Return, Tai Ma of the Virginia Polytechnic Institute: and State
It is suspected that the environmental temperature in which batteries are activated affects their life. Thirty homogeneous batteries were tested six at each of five temperatures, and the data are shown below (activated life in seconds). Analyze and interpret the data. (C. R. Hicks, Fundamental
Do Duncan's test for paired comparisons for the data of Exercise 13.8. Discuss the results.
Show that the computing formula for SSB, in the analysis of variance of the randomized complete block design, is equivalent to the corresponding term in the identity ofTheorem.
For the randomized block design with k treatments and b blocks, showthat
Four kinds of fertilizer f1, f2, f3, and f4 are used to study the yield of beans. The soil is divided into 3 blocks each containing 4 homogeneous plots. The yields in kilograms per plot and the corresponding treatments are as follows:(a) Conduct an analysis of variance at the 0.05 level of
Three varieties of potatoes are being compared for yield. The experiment is conducted by assigning each variety at random to 3 equal-size plots at each of 4 different locations. The following yields for varieties A, B, and C, in 100 kilograms per plot, were recorded. Perform a randomized block
The following data are the percents of foreign additives measured by 5 analysts for 3 similar brands of strawberry jam, A, B, and C. Perform the analysis of variance and test the hypothesis, at the 0.05 level of significance, that the percent of foreign additives is the same for all 3 brands of
The following data represent the final grades obtained by 5 students in mathematics, English, French, and biology. Test the hypothesis that the courses are of equal difficulty. Use a P-value in your conclusions and discuss yourfindings.
In a study on The Periphyton of the South River, Virginia: Mercury Concentration, Productivity, and Autotropic Index Studies conducted, by the Department of Environmental Sciences and Engineering at the Virginia Polytechnic Institute and State University, the total mercury concentration in
A nuclear power facility produces a vast amount of heat which is usually discharged into aquatic systems. This heat raises the temperature of the aquatic system, resulting in a greater concentration of chlorophyll o, which in turn extends the growing season. To study this effect, water samples were
In a study conducted by the Department of Health and Physical Education at the Virginia Polytechnic Institute and State University, 3 diets were assigned for a period of 3 days to each of 6 subjects in a randomized block design. The subjects, playing the role of blocks, were assigned the following
Organic arsenicals are used by forestry personnel as silvicides. The amount of arsenic that is taken into the body when exposed to these silvicides is a major health problem. It is important that the amount of exposure be determined quickly so that a field worker with a high level of arsenic can be
Scientists in the Department of Plant Pathology at Virginia Tech devised an experiment in which 5 different treatments were applied to 6 different locations in an apple orchard to determine if there were significant differences in growth among the treatments. Treatments 1 through 4 represent
In the paper "Self-Control and Therapist Control in the Behavioral Treatment of OverweightWomen" published in Behavioral Research and Therapy (Vol. 10, 1972), two reduction treatments and a control treatment were studied for their effects on the weight change of obese women. The two reduction
Verify the sum-of-squares identity of Theorem.
For the r x r Latin square design, show that
The mathematics department of a large university wishes to evaluate the teaching capabilities of 4 professors. In order to eliminate any effects due to different mathematics courses and different times of the day, it was decided to conduct an experiment using a Latin square design in which the
A manufacturing firm wants to investigate the effects of 5 color additives on the setting time of a new concrete mix. Variations in the setting times can be expected from day-to-day changes in temperature and humidity and also from the different workers who prepare the test molds. To eliminate
In the book Design of Experiments for the Quality Improvement published by the Japanese Standards Association (1989), a study on the amount of dye needed to get the best color for a certain type of a fabric was conducted. The three amounts of dye, 1/3% wof (1/3% of the weight of a fabric), 1% wof,
An experiment was conducted to compare three types of coating materials for copper wire. The purpose of the coating is to eliminate "flaws" in the wire. Ten different specimens of length five millimeters were randomly assigned to receive each coating process and the thirty specimens were subjected
The following data show the effect of 4 operators, chosen randomly, on the output of a particular machine:(a) Perform a model II analysis of variance at the 0.05 level of significance.(b) Compute an estimate of the operator variance component and the experimental error variancecomponent.
Assuming a random effects model, show that E (SSB) = (b – 1) σ2 + k (b – 1) σ23 for the randomized complete block design.
An experiment is conducted in which 4 treatments are to be compared in 5 blocks. The following data are generated:(a) Assuming a random effects model, test the hypothesis at the 0.05 level of significance that there is no difference between treatment means.(b) Compute estimates of the treatment and
Assuming a random effects model, show that E (SST r) = (r – 1) (σ2 + rσ2r) for the Latin square design.
(a) Using a regression approach for the randomized complete block design, obtain the normal equations Ab = g in matrix form. (b) Show that R (β1, β2. β b ׀α1, α α k), = SSB.
Showing 2200 - 2300
of 88243
First
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Last
Step by Step Answers
Get 50% OFF
Claim Now
