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mathematics
applied statistics and probability
Applied Statistics And Probability For Engineers 6th Edition Douglas C. Montgomery, George C. Runger - Solutions
A computer system uses passwords that are exactly seven characters, and each character is one of the 26 letters (a–z) or 10 integers (0–9). Uppercase letters are not used.(a) How many passwords are possible?(b) If a password consists of exactly 6 letters and 1 number, how many passwords are
A batch contains 36 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Of the cells, 6 are selected at random, without replacement, to be checked for replication.(a) What is the probability that all 6 of the selected cells are able to replicate?(b) What is the
An article in Genome Research [€œAn Assessment of Gene Prediction Accuracy in Large DNA Sequences€ (2000, Vol. 10, pp. 1631€“1642)], considered the accuracy of commercial software to predict nucleotides in gene sequences. The following table shows the number
Energy released from cells breaks the molecular bond and converts ATP (adenosine triphosphate) into ADP (adenosine diphosphate). Storage of ATP in muscle cells (even for an athlete) can sustain maximal muscle power only for less than five seconds (a short dash). Three systems are used to replenish
A congested computer network has a 0.002 probability of losing a data packet, and packet losses are independent events. A lost packet must be resent.(a) What is the probability that an e-mail message with 100 packets will need to be resent?(b) What is the probability that an e-mail message with 3
A researcher receives 100 containers of oxygen. Of those containers, 20 have oxygen that is not ionized, and the rest are ionized. Two samples are randomly selected, without replacement, from the lot.(a) What is the probability that the first one selected is not ionized?(b) What is the probability
Shafts are classified in terms of the machine tool that was used for manufacturing the shaft and conformance to surface finish and roundness.(a) If a shaft is selected at random, what is the probability that the shaft conforms to surface finish requirements or to roundness requirements or is from
The probabilities of poor print quality given no printer problem, misaligned paper, high ink viscosity, or printer-head debris are 0, 0.3, 0.4, and 0.6, respectively. The probabilities of no printer problem, misaligned paper, high ink viscosity, or printer-head debris are 0.8, 0.02, 0.08, and 0.1,
An e-mail filter is planned to separate valid e-mails from spam. The word free occurs in 60% of the spam messages and only 4% of the valid messages. Also, 20% of the messages are spam. Determine the following probabilities:(a) The message contains free.(b) The message is spam given
The article [“Clinical and Radiographic Outcomes of Four Different Treatment Strategies in Patients with Early Rheumatoid Arthritis,” Arthritis & Rheumatism (2005, Vol. 52, pp. 3381– 3390)] considered four treatment groups. The groups consisted of patients with different drug
Two Web colors are used for a site advertisement. If a site visitor arrives from an affiliate, the probabilities of the blue or green colors being used in the advertisement are 0.8 and 0.2, respectively. If the site visitor arrives from a search site, the probabilities of blue and green colors in
Consider the well failure data given below. Use Bayes€™ theorem to calculate the probability that a randomly selected well is in the gneiss group given that the well has failed. Wells Failed Geological Formation Group Total Gneiss 170 1685 Granite 28 Loch raven schist 443 3733 Mafic
Consider the hospital emergency room data given below. Use Bayes€™ theorem to calculate the probability that a person visits hospital 4 given they are LWBS. Hospital Total 5640 Total 6991 4329 22,252 5292 LWBS 242 953 246 270 195 1277 1558 4485 984 666 Admitted Not admitted 3820 5163 4728
Consider the endothermic reactions given below. Use Bayes€™ theorem to calculate the probability that a reaction's final temperature is 271 K or less given that the heat absorbed is above target. Final Temperature Conditions Heat Absorbed (cal) Below Target Above Target 266 K 12 40 271 K
The following table provides data on wafers categorized by location and contamination levels. More generally, let the number of wafers with low contamination from the center and edge locations be denoted as nlcand nle, respectively. Similarly, let nhcand
The following table provides data on wafers categorized by location and contamination levels. Let A denote the event that contamination is low, and let B denote the event that the location is center. Are A and B independent? Why or why not?
An integrated circuit contains 10 million logic gates (each can be a logical AND or OR circuit). Assume the probability of a gate failure is p and that the failures are independent. The integrated circuit fails to function if any gate fails. Determine the value for p so that the probability that
Consider the code 39 is a common bar code system that consists of narrow and wide bars(black) separated by either wide or narrow spaces (white). Each character contains nine elements (five bars and four spaces). The code for a character starts and ends with a bar (either narrow or wide) and a
A Web ad can be designed from four different colors, three font types, five font sizes, three images, and five text phrases. A specific design is randomly generated by the Web server when you visit the site. Let A denote the event that the design color is red, and let B denote the event that the
A Web ad can be designed from four different colors, three font types, five font sizes, three images, and five text phrases. A specific design is randomly generated by the Web server when you visit the site. Let A denote the event that the design color is red, and let B denote the event that the
Consider the endothermic reactions given below. Let A denote the event that a reaction's final temperature is 271 K or less. Let B denote the event that the heat absorbed is above target. Use the addition rules to calculate the following probabilities.(a) P(AÈB)(b) P(AÇB¢)(c)
A computer system uses passwords that are six characters, and each character is one of the 26 letters (a–z) or 10 integers (0–9). Uppercase letters are not used. Let A denote the event that a password begins with a vowel (either a, e, i, o, or u), and let B denote the event that a password ends
Strands of copper wire from a manufacturer are analyzed for strength and conductivity. The results from 100 strands are as follows:(a) If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high?(b) If a strand is randomly selected, what is the
In the article “ACL Reconstruction Using Bone-Patellar Tendon-Bone Press-Fit Fixation: 10-Year Clinical Results” in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 248–255), the following causes for knee injuries were considered:Activity
A computer system uses passwords that contain exactly eight characters, and each character is one of 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords with
Suppose that a patient is selected randomly from the those described ,The article “Term Efficacy of Ribavirin Plus Interferon Alfa in the Treatment of Chronic Hepatitis C,” [Gastroenterology (1996, Vol. 111, no. 5, pp. 1307–1312)], considered the effect of two treatments and a control for
A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to schedule three knee, four hip, and five shoulder surgeries. Assume that all schedules are equally likely.Determine the probability for each of the following:(a)
Consider the bar code 39 is a common bar code system that consists of narrow and wide bars (black) separated by either wide or narrow spaces (white). Each character contains nine elements (five bars and four spaces). The code for a character starts and ends with a bar (either narrow or wide) and a
Consider the well failure data is given below. Let A denote the event that the geological formation has more than 1000 wells, and let B denote the event that a well failed. Determine the following probabilities.(a) P(AÇB)(b) P(A¢)(c) P(AÈB)(d) P(AÈB¢)(e) P(A¢ÇB¢)
Consider the hospital emergency room data is given below. Let A denote the event that a visit is to hospital 4, and let B denote the event that a visit results in LWBS (at any hospital).Determine the following probabilities.(a) P(AÇB)(b) P(A¢)(c) P(AÈB)(d) P(AÈB¢)(e) P(A¢ÇB¢)
A Web ad can be designed from four different colors, three font types, five font sizes, three images, and five text phrases. A specific design is randomly generated by the Web server when you visit the site. If you visit the site five times, what is the probability that you will not see the same
Consider the endothermic reaction’s table given below. Let A denote the event that a reaction's final temperature is 271 K or less. Let B denote the event that the heat absorbed is above target.Determine the following probabilities.(a) P(AÇB)(b) P(A')(c)P(AÈB)(d) P(AÈB')(e)
An article in the Journal of Database Management [“Experimental Study of a Self-Tuning Algorithm for DBMS Buffer Pools” (2005, Vol. 16, pp. 1–20)] provided the workload used in the TPC-C OLTP (Transaction Processing Performance Council’s Version C On-Line Transaction Processing) benchmark,
Magnesium alkyls are used as homogenous catalysts in the production of linear low-density polyethylene (LLDPE), which requires a finer magnesium powder to sustain a reaction. Redox reaction experiments using four different amounts of magnesium powder are performed. Each result may or may not be
In a NiCd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation states and that is usually found in the following states:Nickel Charge Proportions
In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Because acids and bases are usually colorless (as are the water and salt produced in the neutralization reaction), pH is measured to monitor the reaction. Suppose that the
A computer system uses passwords that contain exactly eight characters, and each character is 1 of the 26 lowercase letters (a–z) or 26 uppercase letters (A–Z) or 10 integers (0–9). Let Ω denote the set of all possible passwords, and let A and B denote the events that consist of passwords
Consider the bar code in Example 2-12. One code is still held back as a delimiter. For each of the following cases, how many characters can be encoded?(a) The constraint of exactly two wide bars is replaced with one that requires exactly one wide bar.(b) The constraint of exactly two wide bars is
A hospital operating room needs to schedule three knee surgeries and two hip surgeries in a day. Suppose that an operating room needs to handle three knee, four hip, and five shoulder surgeries.(a) How many different sequences are possible?(b) How many different sequences have all hip, knee,
An article in The Journal of Data Science [“A Statistical Analysis of Well Failures in Baltimore County” (2009, Vol. 7, pp. 111–127)] provided the following table of well failures for different geological formation groups in Baltimore County.Let A denote the event that the
Consider the hospital emergency department data given below. Let A denote the event that a visit is to hospital 1, and let B denote the event that a visit results in admittance to any hospital. Determine the number of persons in each of the following
A Web ad can be designed from four different colors, three font types, five font sizes, three images, and five text phrases. How many different designs are possible?
The following table summarizes 204 endothermic reactions involving sodium bicarbonate.Let A denote the event that a reaction€™s final temperature is 271 K or less. Let B denote the event that the heat absorbed is below target. Determine the number of reactions in each of the following
Consider the design of a communication system.(a) How many three-digit phone prefixes that are used to represent a particular geographic area (such as an area code) can be created from the digits 0 through 9?(b) As in part (a), how many three-digit phone prefixes are possible that do not start with
A wireless garage door opener has a code determined by the up or down setting of 12 switches. How many outcomes are in the sample space of possible codes?
In control replication, cells are replicated over a period of two days. Not until mitosis is completed can freshly synthesized DNA be replicated again. Two control mechanisms have been identified—one positive and one negative. Suppose that a replication is observed in three cells. Let A denote
In light-dependent photosynthesis, light quality refers to the wavelengths of light that are important. The wavelength of a sample of photo synthetically active radiations (PAR) is measured to the nearest nanometer. The red range is 675–700 nm and the blue range is 450–500 nm. Let A denote the
Calls are repeatedly placed to a busy phone line until a connection is achieved.Provide a reasonable description of the sample space for each of the random experiments. There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.
An order for an automobile can specify either an automatic or a standard transmission, either with or without air conditioning, and with any one of the four colors red, blue, black, or white. Describe the set of possible orders for this experiment.Provide a reasonable description of the sample
The time of a chemical reaction is recorded to the nearest millisecond.Provide a reasonable description of the sample space for each of the random experiments. There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.
The voids in a ferrite slab are classified as small, medium, or large. The number of voids in each category is measured by an optical inspection of a sample.Provide a reasonable description of the sample space for each of the random experiments. There can be more than one acceptable interpretation
The pH reading of a water sample to the nearest tenth of a unit.Provide a reasonable description of the sample space for each of the random experiments. There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.
The time until a service transaction is requested of a computer to the nearest millisecond.Provide a reasonable description of the sample space for each of the random experiments. There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.
The concentration of ozone to the nearest part per billion.Provide a reasonable description of the sample space for each of the random experiments. There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.
A scale that displays two decimal places is used to measure material feeds in a chemical plant in tons.Provide a reasonable description of the sample space for each of the random experiments. There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.
Each of 24 Web sites is classified as containing or not containing banner ads.Provide a reasonable description of the sample space for each of the random experiments. There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.
The number of hits (views) is recorded at a high-volume Web site in a day.Provide a reasonable description of the sample space. There can be more than one acceptable interpretation of each experiment. Describe any assumptions you make.
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