- a. Suppose that $68,000 is to be allocated for advertising, research, and investment in the ratio 8:6:3. How much money will be allocated for each
- A quality characteristic of interest for a coffee-bag-filling process is the weight of the coffee in the individual bags. If the bags are under
- An apple juice bottling company maintains records concerning the number of unacceptable bottles of juice obtained from the filling and capping
- According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common
- Compute a 95% confidence interval for the population mean, based on the sample 10, 12, 13, 14, 15, 16, and 49. Change the number from 49 to 16 and
- The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each
- A large candy manufacturer is concerned that the mean weight of their bag of Gooey Sour Worms is not greater than 7.3 ounces. It can be assumed that
- Each of the possible five outcomes of a random experiment is equally likely. The sample space is {a, b, c, d, e}. Let A denote the event {a, b}, and
- The sample space of a random experiment is {a, b, c, d, e} with probabilities 0.1, 0.1, 0.2, 0.4, and 0.2, respectively. Let A denote the event {a,
- A part selected for testing is equally likely to have been produced on any one of six cutting tools. (a) What is the sample space? (b) What is the
- An injection-molded part is equally likely to be obtained from any one of the eight cavities on a mold. (a) What is the sample space? (b) What is
- A sample space contains 20 equally likely outcomes. If the probability of event A is 0.3, how many outcomes are in event A?
- Orders for a computer are summarized by the optional features that are requested as follows: Proportion of orders No optional features
- If the last digit of a weight measurement is equally likely to be any of the digits 0 through 9, (a) What is the probability that the last digit is
- A sample preparation for a chemical measurement is completed correctly by 25% of the lab technicians, completed with a minor error by 70%, and
- A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly, what is the
- Suppose your vehicle is licensed in a state that issues license plates that consist of three digits (between 0 and 9) followed by three letters
- A message can follow different paths through servers on a network. The senders message can go to one of five servers for the first step, each of them
- Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as
- Samples of a Fast aluminum part are classified on the basis of surface finish (in micro inches) and edge finish. The results of 100 parts are
- Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized
- Use the axioms of probability to show the following: (a) For any event. E, P (E’) = 1 – P (E). (b) P (Ø) = 0 (c) If A is contained in B, then
- If P (A) = 0.3, P (B) = 0.2, and P (A U B) = 0.1, determine the following probabilities: (a) P (A’) (b) P (A U B) (c) P (A` ∩ B) (d) P
- If A, B, and C are mutually exclusive events with P(A) = 0.2, P (B) =0.3, and P(C) = 0.4, determine the following probabilities: (a) P (A U B U
- If A, B, and C are mutually exclusive events, is it possible for P (A) = 0.3, P (B) = 0.4, and P (C) = 0.5? Why or why not?
- Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as
- The analysis of shafts for a compressor is summarized by conformance to specifications. Roundness conforms Yes No Surface finish yes
- Cooking oil is produced in two main varieties: mono-and polyunsaturated. Two common sources of cooking oil are corn and canola. The following table
- A manufacturer of front lights for automobiles tests lamps under a high humidity, high temperature environment using intensity and useful life as the
- The shafts in Exercise 2-53 are further classified in terms of the machine tool that was used for manufacturing the shaft.
- Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows:
- Samples of a cast aluminum part are classified on the basis of surface finish (in micro inches) and length measurements. The results of 100 parts are
- The analysis of shafts for a compressor is summarized by conformance to specifications:
- The following table summarizes the analysis of samples of galvanized steel for coating weight and surface roughness
- Consider the data on wafer contamination and location in the sputtering tool shown in Table 2-2. Assume that one wafer is selected at random from
- A lot of 100 semiconductor chips contains 20 that are defective. Two are selected randomly, without replacement, from the lot. (a) What is the
- 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
- Continuation of Exercise 2-63. Suppose three castings are selected at random, without replacement, from the lot of 40. In addition to the definitions
- A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement from the
- Continuation of Exercise 2-65. Three containers are selected, at random, without replacement, from the batch. (a) What is the probability that the
- A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioning systems:
- If P (A|B) = 1, must A = B? Draw a Venn diagram to explain your answer.
- Suppose A and B are mutually exclusive events. Construct a Venn diagram that contains the three events A, B, and C such that P (A|C) _ 1 and P (B) C)
- Suppose that P (A|B) = 0.4 and P(B) = 0.5. Determine the following: (a) P (A ∩ B) (b) P (A’ ∩ B)
- Suppose that and P(A)|B) = 0.2, (PA|B’) = 0.3, and P(B) = 0.8. What is P (A)?
- 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
- 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.
- In the manufacturing of a chemical adhesive, 3% of all batches have raw materials from two different lots. This occurs when holding tanks are
- 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
- 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
- Incoming calls to a customer service center are classified as complaints (75% of call) or requests for information (25% of calls). Of the complaints,
- Computer keyboard failures are due to faulty electrical connects (12%) or mechanical defects (88%). Mechanical defects are related to loose keys
- A batch of 25 injection-molded parts contains 5 that have suffered excessive shrinkage. (a) If two parts are selected at random, and without
- A lot of 100 semiconductor chips contains 20 that are defective. (a) Two are selected, at random, without replacement, from the lot. Determine the
- If P (A|B) = 0.4, P (B) = 0.8, P (A) = 0.5, are the events A and B independent?
- If P (A|B) = 0.3, P (B) = 0.8, P (A) = 0.3, and are the events B and the complement of A independent?
- Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as
- Samples of a cast aluminum part are classified on the basis of surface finish (in micro inches) and length measurements. The results of 100 parts are
- Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized
- If P (A) = 0.2, P (B) = 0.2, and A and B are mutually exclusive, are they independent?
- The probability that a lab specimen contains high levels of contamination is 0.10. Five samples are checked, and the samples are independent. (a)
- 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
- Eight cavities in an injection-molding tool produce plastic connectors that fall into a common stream. A sample is chosen every several minutes.
- 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
- 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
- An optical storage device uses and error recovery Procedure that requires an immediate satisfactory readback of any written data. If the readback is
- A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement, from the batch.
- Suppose that P (A|B) = 0.7, P (A) = 0.5, and P (B) = 0.2. Determine P (B|A).
- 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
- Semiconductor lasers used in optical storage products require higher power levels for write operations than for read operations. High-power-level
- Customers are used to evaluate preliminary product designs. In the past, 95% of highly successful products received good reviews, 60% of moderately
- An inspector working for a manufacturing company has a 99% chance of correctly identifying defective items and a 0.5% chance of incorrectly
- A new analytical method to detect pollutants in water is being tested. This new method of chemical analysis is important because, if adopted, it
- Decide whether a discrete or continuous random variable is the best model for each of the following variables: (a) The time until a projectile
- 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
- The data from 200 machined parts are summarized as follows: Depth of bore Above Below Edge condition Target Target Coarse
- Computers in a shipment of 100 units contain a portable hard drive, CD RW drive, or both according to the following table: Portable hard
- 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
- Let E1, E2, and E3 denote the samples that conform to a percentage of solids specification, a molecular weight specification, and a color
- 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
- 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
- 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 getting through by telephone to buy concert tickets is 0.92. For the same event, the probability of accessing the vendor’s Web
- The British government has stepped up its information campaign regarding foot and mouth disease by mailing brochures to farmers around the country.
- 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
- An encryption-decryption system consists of three elements: encode, transmit, and decode. A faulty encode occurs in 0.5% of the messages processed,
- 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
- A robotic insertion tool contains 10 primary components. The probability that any component fails during the warranty period is 0.01. Assume that 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
- 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
- A lot of 50 spacing washers contains 30 washers that are thicker than the target dimension. Suppose that three washers are selected at random,
- Continuation of Exercise 2-117. Washers are selected from the lot at random, without replacement. (a) What is the minimum number of washers that
- The following table lists the history of 940 orders for features in an entry-level computer product. Extra memory No
- 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
- 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
- A company that tracks the use of its web site determined that the more pages a visitor views, the more likely the visitor are to provide contact
- An order for a personal digital assistant can specify any one of five memory sizes, any one of three types of displays, any one of four sizes of a
- In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are three machine tools, four polishing tools, and
- New designs for a wastewater treatment tank have proposed three possible shapes, four possible sizes, three locations for input valves, and four
- A manufacturing process consists of 10 operations that can be completed in any order. How many different production sequences are possible?