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mathematics
statistics

Questions and Answers of Statistics

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 b. Computer Warehouse sells batteries ($2) and
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 filled, two problems arise. First, customers may not
An apple juice bottling company maintains records concerning the number of unacceptable bottles of juice obtained from the filling and capping machines. Based on past data, the probability that a
According to Investment Digest ("Diversification and the Risk/Reward Relationship", Winter 1994, 1-3), the mean of the annual return for common stocks from 1926 to 1992 was 15.4%, and the standard
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 recalculate the confidence interval. Using the
The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester. A sample of 25 students enrolled in the
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 the population standard deviation is .5 ounces
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 let B denote the event {c, d, e}. Determine the
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, b, c}, and let B denote the event {c, d, e}.
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 probability that the part is from tool 1? (c)
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 the probability a part is from cavity 1 or 2? (c)
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 0.3 One optional feature
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 0? (b) What is the probability that the last
A sample preparation for a chemical measurement is completed correctly by 25% of the lab technicians, completed with a minor error by 70%, and completed with a major error by 5%. (a) If a
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 probability that it is a valid number?
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 (between A and Z). If a license number is selected
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 can send to five servers at the second step, each
Disks of polycarbonate plastic from a supplier are analyzed for scratch and shock resistance. The results from 100 disks are summarized as follows: Shock resistance High
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 summarized as follows: Edge
Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows:
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 P (A) < P (B)
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 (A ∩ B’) (e) P [(A U B’)] (f) P (A` U B)
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 C) (b) P (A ∩ B ∩ C) (c) P (A ∩ B)
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 follows: Shock resistance High Low Scratch
The analysis of shafts for a compressor is summarized by conformance to specifications. Roundness conforms Yes No Surface finish yes 345 5 Conforms no 12 8 (a) If a shaft
Cooking oil is produced in two main varieties: mono-and polyunsaturated. Two common sources of cooking oil are corn and canola. The following table shows the number of bottles of these oils at a
A manufacturer of front lights for automobiles tests lamps under a high humidity, high temperature environment using intensity and useful life as the responses of interest. The following table shows
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 summarized as follows:
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 this set. Let A denote the event that a wafer
A lot of 100 semiconductor chips contains 20 that are defective. Two are selected randomly, without replacement, from the lot. (a) What is the probability that the first one selected is
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
Continuation of Exercise 2-63. Suppose three castings are selected at random, without replacement, from the lot of 40. In addition to the definitions of events A and B, let C denote the event that
A batch of 500 containers for frozen orange juice contains 5 that are defective. Two are selected, at random, without replacement from the batch. (a) What is the probability that the second one
Continuation of Exercise 2-65. Three containers are selected, at random, without replacement, from the batch. (a) What is the probability that the third one selected is defective given 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) = 0?
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 wet, the probability of a failure during the
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
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
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
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
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
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
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
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
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 follows: Shock resistance High Low Scratch
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 summarized as
Samples of emissions from three suppliers are classified for conformance to air-quality specifications. The results from 100 samples are summarized as follows: Conforms
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) What is the probability that none contains high
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
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 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
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
An optical storage device uses and error recovery Procedure that requires an immediate satisfactory readback of any written data. If the readback is not successful after three writing operations,
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
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 legitimate users originate calls from two or more
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
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%
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
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
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
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
The data from 200 machined parts are summarized as follows: Depth of bore Above Below Edge condition Target Target Coarse 15 10 Moderate 25 20 Smooth
Computers in a shipment of 100 units contain a portable hard drive, CD RW drive, or both according to the following table: Portable hard drive Yes No CD RW Yes 15
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
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
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 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
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
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 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
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
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,
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
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
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 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
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
Continuation of Exercise 2-117. 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 following table lists the history of 940 orders for features in an entry-level computer product. Extra memory No Yes Optional high- no 514 68 Speed processor yes
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 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
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 information. Use the following tables to answer the
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 hard disk, and can either include or not include a
In a manufacturing operation, a part is produced by machining, polishing, and painting. If there are three machine tools, four polishing tools, and three painting tools, how many different routings
New designs for a wastewater treatment tank have proposed three possible shapes, four possible sizes, three locations for input valves, and four locations for output valves. How many different
A manufacturing process consists of 10 operations that can be completed in any order. How many different production sequences are possible?

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