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applied statistics and multivariate

Applied Statistics And Probability For Engineers 5th Edition Douglas C. Montgomery, George C. Runger - Solutions

Calculate the mean and variance for the random variable in Exercise 3.29.
Calculate the mean and variance for the random variable in Exercise 3.28.
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) bench- mark, which
Trees are subjected to different levels of carbon dioxide atmosphere with 6% of the trees in a minimal growth condition at 350 parts per million (ppm), 10% at 450 ppm (slow growth). 47% at 550 ppm (moderate growth), and 37% at 650 ppm (rapid growth). What are the mean and standard deviation of the
The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent com- puters working in parallel. At each critical step, the comput- ers "vote" to determine the appropriate step. The probability that a computer will ask for a roll to the left when a roll to
In a NiCd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation states. Assume the following proportions of the states: Nickel Charge 0 Proportions Found 0.17 0.35 0.33 0.15(a) Determine the cumulative distribution function of nickel
Determine the mean and variance of the random variable in Exercise 3-18
Determine the mean and variance of the random variable in Exercise 3.16.
Determine the mean and variance of the random variable in Exercise 3.14.
Determine the cumulative distribution function for the random variable in Exercise 3-16; also determine the following probabilities: (a) PX1.5) (b) P(X3) (c) PX2) (d) P1 Determine each of the following probabilities: (a) P(X 4) (b) P(X>7) (d) P(X4) (c) P(X5) (e) P(X 2)
Determine the cumulative distribution function for the random variable in Exercise 3-15; also determine the fol- lowing probabilities: (a) P(X1.25) (b) P(X2.2) (c) P(-1.1 0)
Determine the cumulative distribution function of the random variable in Exercise 3-14.
Actual lengths of stay at a hospital's emergency de- partment in 2009 are shown in the following table (rounded to the nearest hour). Length of stay is the total of wait and service times. Some longer stays are also approximated as 15 hours in this table.
The data from 200 endothermic reactions involving sodium bicarbonate are summarized as follows: Final Temperature Conditions Number of Reactions 266 K 271 K 274 K 60 92 Calculate the probability mass function of final temperature.
The distributor of a machine for cytogenics has developed a new model. The company estimates that when it is introduced into the market, it will be very successful with a probability 0.6, moderately successful with a probability 0.3, and not successful with probability 0.1. The estimated yearly
A disk drive manufacturer sells storage devices with capacities of one terabyte, 500 gigabytes, and 100 gigabytes with probabilities 0.5, 0.3, and 0.2, respectively. The revenues associated with the sales in that year are estimated to be $50 million, $25 million, and $10 million, respectively. Let
The space shuttle flight control system called PASS (Primary Avionics Software Set) uses four independent computers working in parallel. At each critical step, the computers "vote" to determine the appropriate step. The probability that a computer will ask for a roll to the left when a roll to the
An article in Knee Surgery Sports Traumatology Arthroscopy ["Arthroscopic Meniscal Repair with an Absorbable Screw: Results and Surgical Technique" (2005, Vol. 13.pp. 273-279)] cites a success rate of more than 90% for meniscal tears with a rim width of less than 3 mm, but only a 67% success rate
f(x) = (3/4X1/4), x = 0, 1, 2,... (a) P(X 2) (b) P(X2) (c) P(X>2) (d) P(X = 1)
(x)=2x+x=0.1,2,3,4 (a) P(X = 4) (b) P(X 1) (c) P2X
f(x)=(8/7X1/2), x=1,2,3 (a) P(X 1) (b) P(X> 1) (c) P2 1)
The sample space of a random experiment is (a,b, c,d, e,f, and each outcome is equally likely. A random variable is defined as follows: outcome x a b C d e 0 0 1.5 1.5 2 3 Determine the probability mass function of X. Use the proba- bility mass function to determine the following probabilities: (a)
Wood paneling can be ordered in thicknesses of 1/8, 1/4, or 3/8 inch. The random variable is the total thickness of paneling in two orders.
A batch of 500 machined parts contains 10 that do not conform to customer requirements. The random variable is the number of parts in a sample of five parts that do not conform to customer requirements.
Calculate probabilities, determine means and variances for some common discrete probability distributions
Select an appropriate discrete probability distribution to calculate probabilities in specific applications
Understand the assumptions for some common discrete probability distributions
Calculate means and variances for discrete random variables
Determine probabilities from cumulative distribution functions and cumulative distribution functions from probability mass functions, and the reverse
Determine probabilities from probability mass functions and the reverse
Suppose that a table of part counts is generalized as follows: conforms Do supplier 1 Ja Ab 2 wherea, b, and k are positive integers. Let A denote the event that a part is from supplier I and let B denote the event that a part conforms to specifications. Show that A and B are independent events.
If the events 4 and 8 are independent, show that A and B are independent.
Assume the following characteristics of the inspection process in Exercise 2-177.If an operator checks a bolt, the probability that an incorrectly torqued bolt is identified is 0.95.If a checked bolt is correctly torqued, the operator's conclusion is always correct. What is the probability that at
A biotechnology manufacturing firm can pro- duce diagnostic test kits at a cost of $20. Each kit for which there is a demand in the week of production can be sold for $100. However, the half-life of components in the kit requires the kit to be scrapped if it is not sold in the week of production.
Suppose that a lot of washers is large enough that it can be assumed that the sampling is done with re- placement. Assume that 60% of the washers exceed the target thickness. (a) What is the minimum number of washers that need to be selected so that the probability that none are thicker than the
Suppose documents in a lending organization are selected randomly (without replacement) for review. In a set of 50 documents, suppose that two actually con- tain errors. (a) What is the minimum sample size such that the probability exceeds 0.90 that at least one document in error is selected? (b)
Two suppliers each supplied 2000 parts and these were evaluated for conformance to specifications. One part type was of greater complexity than the other. The proportion of nonconforming parts of each type are shown in the table. Simple Complex Component Assembly Total Supplier 1 Nonconforming 2 10
Natural red hair consists of two genes. People with red hair have two dominant genes, two regressive genes, or one dominant and one regressive gene. A group of 1000 people was categorized as follows: Gene 2 Gene 1 Dominant Regressive Other Dominant 5 25 30 Regressive 7 63 35 Other 20 15 800 Let A
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 six letters and one num- ber, how many passwords are
A batch contains 36 bacteria cells. Assume that 12 of the cells are not capable of cellular replication. Six cells are selected at random, without replacement, to be checked for replication. (a) What is the probability that all six cells of the selected cells are able to replicate? (b) What is the
An article in Genome Research ["An 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 se- quences. The following table shows the number of se- quences for which the programs
A company that tracks the use of its web sine deter- mined that the more pages a visitor views, the more likely the visitor is to provide contact information. Use the following tables to answer the questions: Number of pages viewed: Percentage of visitors: Percentage of visitors in each page-view
The following table lists the history of 940 orders for features in an entry-level computer product. optional high- speed processor yes extra memory yes 514 68 112 246 Let 4 be the event that an order requests the optional high- speed processor, and let & be the event that an order requests extra
Continuation of Exercise 2-187.Washers are se- lected from the lot at random, without replacement.(a) What is the minimum number of washers that need to be selected so that the probability that all the washers are thinner than the target is less than 0.10? (b) What is the minimum number of washers
An e-mail message can travel through one of two server routes. The probability of transmission error in each of the servers and the proportion of messages that travel each route are shown in the following table. Assume that the servers are independent. percentage probability of error of messages
It is known that two defective copies of a commer- cial software program were erroneously sent to a shipping lot that now has a total of 75 copies of the program. A sample of copies will be selected from the lot without replacement.(a) If three copies of the software are inspected, determine the
The following circuit operates if and only if there is a path of functional devices from left to right. Assume devices fail independently and that the probability of failure of each device is as shown. What is the probability that the circuit operates? 0.01 0.01 0.1 0.1 0.1
A steel plate contains 20 bolts. Assume that five bolts are not torqued to the proper limit. Four bolts are selected at random, without replacement, to be checked for torque. (a) What is the probability that all four of the selected bolts are torqued to the proper limit? (b) What is the probability
Transactions to a computer database are either new items or changes to previous items. The addition of an item can be completed in less than 100 milliseconds 90% of the time, but only 20% of changes to a previous item can be com pleted in less than this time. If 30% of transactions are changes,
Let E. E., and E, denote the samples that conform to a percentage of solids specification, a molecular weight specification, and a color specification, respectively. A total of 240 samples are classified by the E., E., and E, specifications, where yes indicates that the sample conforms. Eyes E yes
Computers in a shipment of 100 units contain a portable hard drive, DVD drive, or both, according to the following table: portable hard drive yes no DVD yes 15 80 B 4 Let A denote the event that a computer has a portable hard drive and let B denote the event that a computer has a DVD drive. If one
The data from 200 machined parts are summarized as follows: depth of bore above below odge condition target target coarse 15 10 moderate 25 20 smooth 50 80 (a) What is the probability that a part selected has a moderate edge condition and a below-target bore depth? (b) What is the probability that
A sample preparation for a chemical measurement is completed correctly by 25% of the lab technicians, com- pleted with a minor error by 70%, and completed with a major error by 5% (a) If a technician is selected randomly to complete the prepa- ration, what is the probability it is completed without
Energy released from three 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 only sustain maximal muscle power for less than five seconds (a short dash). Three systems are used to re-
Semiconductor lasers used in optical storage prod- ucts require higher power levels for write operations than for read operations. High-power-level operations lower the useful life of the laser. Lasers in products used for backup of higher-speed mag- netic disks primarily write, and the probability
An optical storage device uses an error recovery pro- cedure that requires an immediate satisfactory readback of any written data. If the readback is not successful after three writing operations, that sector of the disk is eliminated as unacceptable for data storage. On an acceptable portion of
Samples of a cast aluminum part are classified on the basis of surface finish (in micromches) and length mea- surements. The results of 100 parts are summarized as follows: length excellent good surface excellent 80 2 finish good 10 Let 4 denote the event that a sample has excellent surface fin-
A congested computer network has a 0.002 proba- bility 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 any to be resent? (b) What is the probability that an e-mail message
Incoming calls to a customer service center are classi- fied as complaints (75% of calls) or requests for information (25% of calls). Of the complaints, 40% deal with computer equipment that does not respond and 57% deal with incomplete software installation; in the remaining 3% of complaints the
In the manufacturing of a chemical adhesive. 3% of all batches have raw materials from two different lots. This occurs when holding tanks are replenished and the remaining portion of a lot is insufficient to fill the tanks. Only 5% of batches with material from a single lot require reprocessing.
A lot contains 15 castings from a local supplier and 25 castings from a supplier in the next state. Two castings are selected randomly, without replacement, from the lot of 40.Let A be the event that the first casting selected is from the local supplier, and let & denote the event that the second
A researcher receives 100 containers of oxygen. Of those containers, have oxygen that is not ionized, and the rest are ionized. Two samples are randomly selected, without re- placement, from the lot. (a) What is the probability that the first one selected is not ionized? (b) What is the probability
The analysis of shafts for a compressor is summa- rized by conformance to specifications: roundness conforms yes surface finish conforms yes 345 no 12 8 (a) If we know that a shaft conforms to roundness require- ments, what is the probability that it conforms to surface finish requirements? (b) If
If A, B, and C are mutually exclusive events, is it possi ble for P(A) = 0.3, P(B) = 0.4, and P(C)=0.5? Why or why not? roundness conforms Tool 1 yes surface finish yes 200 conforms 4 Tool 2 yes surface finish conforms yes 145 Do 8 I 2 roundness conforms 4 6 (a) If a shaft is selected at random,
Shafts are classified in terms of the machine tool that was used for manufacturing the shaft and conformance to surface finish and roundness.
Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and edge finish. The results of 100 parts are summarized as follows: edge finish excellent good surface finish excellent 80 2 good 10 Let A denote the event that a sample has excellent surface fin- ish,
A sample of three calculators is selected from a manufacturing line, and each calculator is classified as either defective or acceptable. Let A, B, and C denote the events that the first, second, and third calculators, respectively, are defective. (a) Describe the sample space for this experiment
Decide whether a discrete or continuous random variable is the best model for each of the following variables: (a) The time until a projectile returns to earth. (b) The number of times a transistor in a computer memory changes state in one operation. (e) The volume of gasoline that is lost to
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 are 0.8 and 0.2, respectively. If the site visitor arrives from a search site, the blue and green colors are 0.4 and 0.6, re- spectively. The proportions of
Consider the well failure data in Exercise 2-53.Use Bayes' Theorem to calculate the probability that a randomly selected well is in the gneiss group given that the well is failed.
Consider the hospital emergency room data in Example 2-8.Use Bayes' Theorem to calculate the probability that a person visits Hospital 4 given they are LWBS.
Consider the endothermic reactions in Exercise 2-50.Use Bayes Theorem to calculate the probability that a reaction final temperature is 271 K or less given that the heat absorbed is above target.
A new analytical method to detect pollutants in wa- ter is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminants organic pollutants, volatile solvents, and chlorinated compounds instead of having to use a single
An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly classifying a good item as defec- tive. The company has evidence that its line produces 0.9% of nonconforming items. (a) What is the probability that an item
Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products received good reviews, 60% of moderately successful products received good reviews, and 10% of poor products received good reviews. In addition, 40% of products have been highly successful,
In the 2004 presidential election, exit polls from the critical state of Ohio provided the following results: Bush Kerry no college degree (62%) college graduate (38%) 50% 50% 53% 46% If a randomly selected respondent voted for Bush, what is the probability that the person has a college degree?
A new process of more accurately detecting anaer- obic respiration in cells is being tested. The new process is important due to its high accuracy, its lack of extensive ex- perimentation, and the fact that it could be used to identify five different categories of organisms: obligate anaerobes,
Software to detect fraud in consumer phone cards tracks the number of metropolitan areas where calls originate each day. It is found that 1% of the legitimate users originate calls from two or more metropolitan areas in a single day. However, 30% of fraudulent users originate calls from two or more
Suppose that P(A|B)= 0.4, P(A|B) = 0.2, and P(B) = 0.8.Determine P(B|4).
Suppose that P(A|B) = 0.7.P(4) = 0.5, and P(B) = 0.2.Determine P(B|4).
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 4 denote the event that the design color is red and Let 8 denote the event that the
Consider the well failure data in Exercise 2-53.Let 4 denote the event that the geological formation has more than 1000 wells and let 8 denote the event that a well failed. Are these events independent?
Consider the hospital emergency room data in Example 2-8.Let 4 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). Are these events independent?
Consider the endothermic reactions in Exercise 2-50.Let A denote the event that a reaction final temperature is 271 K or less. Let B denote the event that the heat absorbed is above target. Are these events independent?
The following circuit operates if and only if there is a path of functional devices from left to right. The probability each device functions is as shown. Assume that the probabil- ity that a device functions does not depend on whether or not other devices are functional. What is the probability
The following circuit operates if and only if there is a path of functional devices from left to right. The probability that each device functions is as shown. Assume that the prob ability that a device is functional does not depend on whether or not other devices are functional. What is the
Eight cavities in an injection-molding tool produce plastic connectors that fall into a common stream. A sample is chosen every several minutes. Assume that the samples are independent. (a) What is the probability that five successive samples were all produced in cavity one of the mold? (b) What is
A credit card contains 16 digits. It also contains a month and year of expiration. Suppose there are one million credit card holders with unique card numbers. A hacker ran- domly selects a 16-digit credit card number. (a) What is the probability that it belongs to a user? (b) Suppose a hacker has a
In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Since 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 player of a video game is confronted with a series of four opponents and an 80% probability of defeating each oppo. nent. Assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends) (a) What is the probability that a player defeats
Six tissues are extracted from an ivy plant infested by spider mites. The plant in infested in 20% of its area. Each tissue is chosen from a randomly selected area on the ivy plant. (a) What is the probability that four successive samples show the signs of infestation? (b) What is the probability
In a test of a printed circuit board using a random test pattem, an array of 10 bits is equally likely to be 0 or 1.Assume the bits are independent. (a) What is the probability that all bits are 1s? (b) What is the probability that all bits are (s? (c) What is the probability that exactly five bits
Redundant Array of Inexpensive Disks (RAID) is a technology that uses multiple hard drives to increase the speed of data transfer and provide instant data backup. Suppose that the probability of any hard drive failing in a day is 0.001 and the drive failures are independent. (a) A RAID 0 scheme
Samples of emissions from three suppliers are clas- sified for conformance to air-quality specifications. The re- sults from 100 samples are summarized as follows: supplier 123 2 conforms yes 22 8 25 5 30 10 Let A denote the event that a sample is from supplier 1, and let B denote the event that a
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: scratch resistance shock resistance high low high 70 9 low 16 3 Let A denote the event that a disk has high shock resistance, and let B denote the
A batch of 500 containers for frozen orange juice contains five that are defective. Two are selected, at random, without replacement, from the batch. Let A and B denote the events that the first and second containers selected are defec- tive, respectively. (a) Are 4 and 8 independent events? (b) If
If P(A)=0.2, P(B) = 0.2, and 4 and B are mutu- ally exclusive, are they independent?
If P(A|B)=0.3, P(B) = 0.8, and P(-4) = 0.3, are the events B and the complement of 4 independent?
If P(A|B)=0.4, P(B) = 0.8, and P(4) = 0.5, are the events A and B independent?
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 in randomly generated by the Web server when you visit the site. Determine the probability that the ad color is red and the font size is not the smallest

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