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applied statistics and probability for engineers

Questions and Answers of Applied Statistics And Probability For Engineers

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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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%
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
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
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%
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
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
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
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
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
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
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
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,
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
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
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
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
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
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
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
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
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
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
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
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 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
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
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%
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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

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