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
business
applied statistics and probability for engineers
Applied Statistics And Probability For Engineers 3rd Edition Douglas C. Montgomery, George C. Runger - Solutions
Thickness measurements of a coating process are made to the nearest hundredth of a millimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for this process.
Let the random variable X be equally likely to assume any of the values , , or . Determine the mean and variance of X.
Let the random variable X have a discrete uniform distribution on the integers . Determine the mean and variance of X.
Let the random variable X have a discrete uniform distribution on the integers . Determine the mean and variance of X.
The range of the random variable X is where x is unknown. If each value is equally likely and the mean of X is 6, determine x.
Determine the mean and variance of the random variable in Exercise 3-23..
Determine the mean and variance of the random variable in Exercise 3-22..
Determine the mean and variance of the random variable in Exercise 3-20..
Determine the mean and variance of the random variable in Exercise 3-19..
Determine the mean and variance of the random variable in Exercise 3-17..
Determine the mean and variance of the random variable in Exercise 3-15..
Determine the mean and variance of the random variable in Exercise 3-13..
If the range of X is the set {0, 1, 2, 3, 4} and P(X x) 0.2 determine the mean and variance of the random variable.
The thickness of wood paneling (in inches) that a customer orders is a random variable with the following cumulative distribution function: 0 x < 1/8 0.2 1/8 x 1/4 F(x) = 0.9 1/4 x 3/8 1 3/8 x Determine the following probabilities: (a) P(X 1/18) (b) P(X 1/4) (c) P(X 5/16) (d) P(X > 1/4) (e) P(X
Errors in an experimental transmission channel are found when the transmission is checked by a certifier that detects missing pulses. The number of errors found in an eightbit byte is a random variable with the following distribution: 0 0.7 F(x) = 0.9 1 x
Determine the cumulative distribution function for the variable in Exercise 3-23..Verify that the following functions are cumulative distribution functions, and determine the probability mass function and the requested probabilities. 3-33. F(x)= 0.5 (a) P(X 3) 1 x
Determine the cumulative distribution function for the random variable in Exercise 3-22..
Determine the cumulative distribution function for the random variable in Exercise 3-20..
Determine the cumulative distribution function for the random variable in Exercise 3-19..
Determine the cumulative distribution function for the random variable in Exercise 3-17; also determine the following probabilities:(a) P1X 1.52 (b) P1X 32(c) P1X 22 (d) P11 X 22
Determine the cumulative distribution function for the random variable in Exercise 3-15; also determine the following probabilities:(a) P1X 1.252 (b) P1X 2.22(c) P11.1 X 12 (d) P1X 02
Determine the cumulative distribution function of the random variable in Exercise 3-13.
An assembly consists of three mechanical components.Suppose that the probabilities that the first, second, and third components meet specifications are 0.95, 0.98, and 0.99.Assume that the components are independent. Determine the probability mass function of the number of components in the
An assembly consists of two mechanical components.Suppose that the probabilities that the first and second components meet specifications are 0.95 and 0.98. Assume that the components are independent. Determine the probability mass function of the number of components in the assembly that meet
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
In a semiconductor manufacturing process, three wafers from a lot are tested. Each wafer is classified as pass or fail. Assume that the probability that a wafer passes the test is 0.8 and that wafers are independent. Determine the probability mass function of the number of wafers from a lot that
An optical inspection system is to distinguish among different part types. The probability of a correct classification of any part is 0.98. Suppose that three parts are inspected and that the classifications are independent.Let the random variable X denote the number of parts that are correctly
A disk drive manufacturer estimates that in five years a storage device with 1 terabyte of capacity will sell with probability 0.5, a storage device with 500 gigabytes capacity will sell with a probability 0.3, and a storage device with 100 gigabytes capacity will sell with probability 0.2. The
Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $10
Verify that the following functions are probability mass functions, and determine the requested probabilities. x -2 -10 1 2 f(x) 1/8 2/8 2/8 2/8 1/8
Use the probability mass function in Exercise 3-11 to determine the following probabilities: (a) P(X = 1.5) (c) P(X > 3) (e) P(X=0 or X = 2) (b) P(0.5
The sample space of a random experiment is {a,b, c,d,e, f }, and each outcome is equally likely. Arandom variable is defined as follows:Determine the probability mass function of X. outcome X a b C d e f 0 0 1.5 1.5 2 3
A software program has 5000 lines of code. The random variable is the number of lines with a fatal error.
A group of 10,000 people are tested for a gene called Ifi202 that has been found to increase the risk for lupus.The random variable is the number of people who carry the gene.
Wood paneling can be ordered in thicknesses of 18, 14, or 38 inch. The random variable is the total thickness of paneling in two orders.
An order for an automobile can select the base model or add any number of 15 options. The random variable is the number of options selected in an order.
The random variable is the number of computer clock cycles required to complete a selected arithmetic calculation.
The random variable is the number of surface flaws in a large coil of galvanized steel.
The random variable is the moisture content of a lot of raw material, measured to the nearest percentage point.
A batch of 500 machined parts contains 10 that do not conform to customer requirements. Parts are selected successively, without replacement, until a nonconforming part is obtained. The random variable is the number of parts selected.
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 5 parts that do not conform to customer requirements.
An electronic scale that displays weights to the nearest pound is used to weigh packages. The display shows only five digits. Any weight greater than the display can indicate is shown as 99999. The random variable is the displayed weight.
In a voice communication system with 50 lines, the random variable is the number of lines in use at a particular time.
The random variable is the number of nonconforming solder connections on a printed circuit board with 1000 connections.
Suppose that a table of part counts is generalized as follows:wherea, b, and k are positive integers. Let A denote the event that a part is from supplier 1 and let B denote the event that a part conforms to specifications. Show that A and B are independent events.This exercise illustrates the
If the events A and B are independent, show that and are independent.
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 least one bolt in the sample of four is identified as being incorrectly
Assume the following characteristics of the inspection process in Exercise
A biotechnology manufacturing firm can produce 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. The
Suppose that a lot of washers is large enough that it can be assumed that the sampling is done with replacement.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 all the washers are thinner than
The alignment between the magnetic tape and head in a magnetic tape storage system affects the performance of the system. Suppose that 10% of the read operations are degraded by skewed alignments, 5% by off-center alignments, 1% by both skewness and offcenter, and the remaining read operations are
A company that tracks the use of its web site determined 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:(a) What is the probability that a visitor to the web site provides contact information?(b)
The following circuit operates if and only if there is a path of functional devices from left to right. Assume that devices fail independently and that the probability of failure of each device is as shown. What is the probability that the circuit does not operate? 0.02 0.01 0.01 0.01 0.01 0.02
The alignment between the magnetic tape and head in a magnetic tape storage system affects the performance of the system. Suppose that 10% of the read operations are degraded by skewed alignments, 5% of the read operations are degraded by off-center alignments, and the remaining read operations are
The following table lists the history of 940 orders for features in an entry-level computer product.Let A be the event that an order requests the optional highspeed processor, and let B be the event that an order requests extra memory. Determine the following probabilities:(e) What is the
Washers are selected 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 that need to be selected so that
Continuation of Exercise
A lot of 50 spacing washers contains 30 washers that are thicker than the target dimension. Suppose that three washers are selected at random, without replacement, from the lot.(a) What is the probability that all three washers are thicker than the target?(b) What is the probability that the third
A machine tool is idle 15% of the time. You request immediate use of the tool on five different occasions during the year. Assume that your requests represent independent events.(a) What is the probability that the tool is idle at the time of all of your requests?(b) What is the probability that
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.(a) What is the probability that a message will
A robotic insertion tool contains 10 primary components.The probability that any component fails during the warranty period is 0.01. Assume that the components fail independently and that the tool fails if any component fails.What is the probability that the tool fails during the warranty period?
It is known that two defective copies of a commercial software program were erroneously sent to a shipping lot that has now 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
An encryption-decryption system consists of three elements: encode, transmit, and decode. A faulty encode occurs in 0.5% of the messages processed, transmission errors occur in 1% of the messages, and a decode error occurs in 0.1% of the messages. Assume the errors are independent.(a) What is the
In an automated filling operation, the probability of an incorrect fill when the process is operated at a low speed is 0.001. When the process is operated at a high speed, the probability of an incorrect fill is 0.01. Assume that 30% of the containers are filled when the process is operated at a
The British government has stepped up its information campaign regarding foot and mouth disease by mailing brochures to farmers around the country. It is estimated that 99%of Scottish farmers who receive the brochure possess enough information to deal with an outbreak of the disease, but only 90%of
The probability of getting through by telephone to buy concert tickets is 0.92. For the same event, the probability of accessing the vendor’s Web site is 0.95. Assume that these two ways to buy tickets are independent. What is the probability that someone who tries to buy tickets through 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 5 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 that
Transactions to a computer database are either new items or changes to previous items. The addition of an item can be completed less than 100 milliseconds 90% of the time, but only 20% of changes to a previous item can be completed in less than this time. If 30% of transactions are changes, what is
Let E1, E2, and E3 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 E1, E2, and E3 specifications, where yes indicates that the sample conforms.(a) Are E1,
The probability that a customer’s order is not shipped on time is 0.05. A particular customer places three orders, and the orders are placed far enough apart in time that they can be considered to be independent events.(a) What is the probability that all are shipped on time?(b) What is the
Computers in a shipment of 100 units contain a portable hard drive, CD RW drive, or both according to the following table:Let A denote the events that a computer has a portable hard drive and let B denote the event that a computer has a CD RW drive. If one computer is selected randomly, compute
The data from 200 machined parts are summarized as follows:(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 part selected has a moderate edge condition or a below-target bore depth?(c) What is the
In circuit testing of printed circuit boards, each board either fails or does not fail the test. A board that fails the test is then checked further to determine which one of five defect types is the primary failure mode. Represent 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.(c) The volume of gasoline that is lost to
A new analytical method to detect pollutants in water 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
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 defective.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,
Semiconductor lasers used in optical storage products 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 magnetic disks primarily write, and the probability that
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
A batch of 500 containers for frozen orange juice contains 5 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 container selected is defective, respectively.(a) Are A and B independent events?(b) If the
An optical storage device uses an error recovery procedure 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 the
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 probability that a device functions does not depend on whether or not other devices are functional. What is the probability that
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 probability 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
In a test of a printed circuit board using a random test pattern, 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 0s?(c) What is the probability that exactly five bits
The probability that a lab specimen contains high levels of contamination is 0.10. Five samples are checked, and the samples are independent.(a) What is the probability that none contains high levels of contamination?(b) What is the probability that exactly one contains high levels of
If P1A2 0.2, P1B2 0.2 and A and B are mutually exclusive, are they independent?
Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows:Let A denote the event that a sample is from supplier 1, and let B denote the event that a sample conforms to specifications.(a) Are events
Samples of a cast aluminum part are classified on the basis of surface finish (in microinches) and length measurements.The results of 100 parts are summarized as follows:Let A denote the event that a sample has excellent surface finish, and let B denote the event that a sample has excellent length.
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:Let A denote the event that a disk has high shock resistance, and let B denote the event that a disk has high scratch resistance.Are events A and B
A lot of 100 semiconductor chips contains 20 that are defective.(a) Two are selected, at random, without replacement, from the lot. Determine the probability that the second chip selected is defective.(b) Three are selected, at random, without replacement, from the lot. Determine the probability
A batch of 25 injection-molded parts contains 5 that have suffered excessive shrinkage.(a) If two parts are selected at random, and without replacement, what is the probability that the second part selected is one with excessive shrinkage?(b) If three parts are selected at random, and without
Computer keyboard failures are due to faulty electrical connects (12%) or mechanical defects (88%). Mechanical defects are related to loose keys (27%) or improper assembly(73%). Electrical connect defects are caused by defective wires (35%), improper connections (13%), or poorly welded wires
Incoming calls to a customer service center are classified as complaints (75% of call) 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; and in the remaining 3% of complaints the
Samples of laboratory glass are in small, light packaging or heavy, large packaging. Suppose that 2 and 1% of the sample shipped in small and large packages, respectively, break during transit. If 60% of the samples are shipped in large packages and 40% are shipped in small packages, what
The edge roughness of slit paper products increases as knife blades wear. Only 1% of products slit with new blades have rough edges, 3% of products slit with blades of average sharpness exhibit roughness, and 5% of products slit with worn blades exhibit roughness. If 25% of the blades in
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.
Suppose 2% of cotton fabric rolls and 3% of nylon fabric rolls contain flaws. Of the rolls used by a manufacturer, 70% are cotton and 30% are nylon. What is the probability that a randomly selected roll used by the manufacturer contains flaws?
The probability is 1% that an electrical connector that is kept dry fails during the warranty period of a portable computer.If the connector is ever wet, the probability of a failure during the warranty period is 5%. If 90% of the connectors are kept dry and 10% are wet, what proportion of
Showing 400 - 500
of 5106
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last
Step by Step Answers
Get 50% OFF
Claim Now
