Miller And Freunds Probability And Statistics For Engineers 9th Edition Richard A. Johnson - Solutions

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The type of graphical charts that allows user to make direct comparisons between various data sets are called A. multiple bar charts B. single bar charts C. paired charts D. non paired data charts
The smallest numerical value is subtracted from largest numerical value and then divided to number of class desired to calculate A. simple class interval B. width of class interval C. number of classes D. manifold class intervals
The process of arranging data on the basis of certain properties in classes or groups is classified as A. classification of data B. reflection of data C. sample of population D. sample observations
If the classification of collected data is based on characteristics such as religion, education and caste, then this is considered as A. open end classification B. time series classification C. qualitative classification D. quantitative classification
The original tables used to represent data are considered as A. dispersion tables B. classification tables C. cumulative tables D. distributed tables
In stem and leaf display diagrams used in exploratory analysis, the leaves are considered as A. leading digits B. dispersed digits C. central digits D. trailing digits
The histograms and pie charts are classified as one dimensional diagrams because only A. length is considered B. width is considered C. length plus width is considered D. breadth is considered
The class frequency is divided by number of observations in the frequency distribution to convert it into A. relative margin distribution B. relative variable distribution C. relative frequency distribution D. relative width distribution
The graphs which represents data on maps are considered as A. cartograms B. picto-graph C. pictograms D. symmetry graph
The classification on the basis of time order is called as A. disclosed classification B. chronological classification C. external classification D. internal classification
The halfway point between the lower class limits and upper class limits is classified as A. nominal mid-point B. class mid-point C. interval mid-point D. ordinal mid-point
The set of raw data arranged in ascending or descending order is called A. ordered array B. nominal array C. ordinal array D. interval array
The classification of data on the geographical basis is also called A. reflected classification B. populated classification C. sampling classification D. spatial classification
The types of histograms includes A. deviation bar charts B. paired bar charts C. grouped charts D. all of above
The frequency distribution which is result of cross classification is called A. bivariate frequency distribution B. univariate frequency distribution C. multi-variables distribution D. close ended distribution
The area diagrams and surface diagrams are other names of A. single dimension diagrams B. two dimensional diagrams C. three dimensional diagrams D. four dimension diagrams
The data table which is presented in tabular form on the basis of single characteristics is classified as A. simple table B. complex table C. percentage table D. interval table
The data table which is presented in tabular form on the basis of two or more simultaneous characteristics is classified as A. percentage table B. interval table C. simple table D. complex table
The type of classification in which class is subdivided into subclasses and subclasses are divided into more classes is considered as A. simple classification B. manifold classification C. rational classification D. reflected classification
The three dimensional diagrams are named as so because they considers both A. length and breadth B. breadth and depth C. depth, length and breadth D. depth and length
The data classification which is based on variables such as production, cost, height and weight is considered as A. qualitative classification B. quantitative classification C. open end classification D. time series classification
The distribution which shows the cumulative figure of all the observations placed below upper limit of classes in distribution is considered as A. cumulative frequency distribution B. upper limit distribution C. class distribution D. cumulative class distribution
The third step in constructing the frequency distribution is to A. select appropriate class intervals B. determine class intervals C. determine class limits D. determine midpoints of classes
The term used to describe frequency curve is A. symmetrical distribution B. symmetry and kurtosis C. kurtosis of distribution D. relative frequency curve
The histograms, pie charts and frequency polygons are all types of A. one dimension diagrams B. two dimension diagrams C. cumulative diagrams D. dispersion diagrams
The exclusive method and inclusive method are ways of classifying data on basis of A. manifold classes B. rational intervals C. class width D. class intervals
The 'less than type distribution' and 'more than type distribution'are types of A. class distribution B. cumulative class distribution C. cumulative frequency distribution D. upper limit distribution
The type of cumulative frequency distribution in which the class intervals are added in bottom to top order is classified as A. more than type distribution B. marginal distribution C. variation distribution D. less than type distribution
Considering the types of diagrams, squares, circles and rectangles are classified as A. cumulative diagram B. dispersion diagrams C. one dimension diagrams D. two dimension diagram
The frequencies of all the specific values of x and y variables with total calculated frequencies are classified as A. variate frequencies B. unconditional frequencies C. conditional frequencies D. marginal frequencies
The general tables of data used to show data in orderly manner is called as A. single characteristics tables B. repository tables C. manifold tables D. double characteristic table
The diagrams used to represent grouped and ungrouped data is classified as A. breadth diagrams B. bar diagrams C. width diagrams D. length diagrams
The classification method in which upper and lower limits of interval is also in class interval itself is called A. exclusive method B. inclusive method C. mid-point method D. ratio method
The summary and presentation of data in tabular form with several non-overlapping classes is referred as A. nominal distribution B. ordinal distribution C. chronological distribution D. frequency distribution
The largest value is 60 and the smallest value is 40 and the number of classes desired is 5 then the class interval is A. 20 B. 4 C. 25 D. 15
The data based on workers salary is as 2500, 2700, 2600, 2800, 2200, 2100, 2000, 2900, 3000, 2800, 2200, 2500, 2700, 2800, 2600 and number of classes desired is 10 then width of class interval is A. 400 B. 300 C. 100 D. 200
The type of cumulative frequency distribution in which the class intervals are added in top to bottom order is classified as A. variation distribution B. less than type distribution C. more than type distribution D. marginal distribution
The classification method in which the upper limit of interval is same as of lower limit class interval is called A. exclusive method B. inclusive method C. mid-point method D. ratio method
In stem and leaf display diagrams used in exploratory analysis, the stems are considered as A. central digits B. trailing digits C. leading digits D. dispersed digits
The discrete variables and continuous variables are two types of A. open end classification B. time series classification C. qualitative classification D. quantitative classification
The diagrams such as cubes and cylinders are classified as A. one dimension diagrams B. two dimension diagram C. three dimensional diagrams D. dispersion diagrams
If the vertical lines are drawn at every point of straight line in frequency polygon then by this way the frequency polygon is transformed into A. width diagram B. length diagram C. histogram D. dimensional bar charts
If the true value of population parameter is 10 and the estimated value of population parameter is 15 then the error of estimation is A. 5 B. 25 C. 0.667 D. 150
The criteria of selecting the point estimator must include the information of A. consistency B. unbiasedness C. efficiency D. all of above
Considering the sample statistic, if the sample statistic mean is not equal to population parameter then sample statistic is considered as A. unbiased estimator B. biased estimator C. interval estimator D. hypothesis estimator
If the critical value of normal standard variable is 0.95 and the standard error of specific statistic 3.5 then the margin of error is A. 2.325 B. 3.325 C. 4.325 D. 5.325
The difference between value of parameter of population and value of unbiased estimator point is classified as A. sampling error B. marginal error C. confidence error D. population error
In confidence interval estimation, the formula of calculating confidence interval is A. point estimate * margin of error B. point estimate ± margin of error C. point estimate - margin of error D. point estimate + margin of error
The knowledge of possible errors, point estimate and the degree of confidence is classified as A. interval estimation B. confidence interval C. hypothesis testing D. both a and b
The distance between the true value of population parameter and estimated value of population parameter is called A. error of central limit B. error of confidence interval C. error of estimation D. error of hypothesis testing
The value of any sample statistic which is used to estimate the parameters of population is classified as A. point estimate B. population estimate C. sample estimate D. parameter estimate
If the sample size is greater than or equal to 30 then the sample standard deviation can be approximated to population standard deviation for the A. known standard deviation B. unknown standard deviation C. standard interval deviation D. population interval theorem
In confidence interval estimation, the interval estimate is also classified as A. confidence efficient B. confidence deviation C. confidence mean D. marginal coefficient
The method in which the sample statistic is used to estimate the value of parameters of population is classified as A. estimation B. valuation C. probability calculation D. limited theorem estimation
Considering the sample size, the sampling distribution standard error decreases when the A. size of sample increases B. size of sample decreases C. margin of error increases D. margin of error decreases
In confidence interval estimation, the confidence efficient is denoted by A. 1 + βB. 1 - βC. 1 - αD. 1 + α
To develop interval estimate of any parameter of population, the value which is added or subtracted from the point estimate is classified as A. margin of efficiency B. margin of consistency C. margin of biasedness D. margin of error
If the point estimate is 8 and the margin of error is 5 then the confidence interval is A. 3 to 13 B. 4 to 14 C. 5 to 15 D. 6 to 16
Considering the sample statistic, if the mean of sampling distribution is equal to population mean then the sample statistic is classified as A. unbiased estimator B. biased estimator C. interval estimator D. hypothesis estimator
If the standard deviation of population 1 is 3 with sample size is 8 and the population 2 standard deviation is 5 with sample size is 7 then the standard deviation of sampling distribution is A. 4.044 B. 3.044 C. 1.044 D. 2.044
For a parameter whose value is unknown, the belief or claim for that parameter is classified as A. parameter claim testing B. expected belief testing C. hypothesis testing D. primary limit testing
The upper and lower boundaries of interval of confidence are classified as A. error biased limits B. marginal limits C. estimate limits D. confidence limits
The range or set of values which have chances to contain value of population parameter with particular confidence level is considered as A. secondary interval estimation B. confidence interval estimate C. population interval estimate D. sample interval estimate
16.29 (Stress-strength models for reliability) An alternative model used in reliability treats the environmental stress as a random variable X, with probability density f (x), and the strength of the component to withstand this stress as an independent random variable Y having probability
16.28 With reference to Exercise 16.26, make (a) a total time on test plot (b) a Weibull plot
16.27 Using the estimates of the parameters of the Weibull model obtained in Exercise 16.26, estimate the probability that this kind of circuit will perform satisfactorily for at least 100 hours.
16.26 To investigate the performance of a logic circuit for a small electronic calculator, a laboratory puts 75 of the circuits on life test without replacement under specified environmental conditions, and the first 10 failures are observed after 28, 46, 50, 63, 81, 101, 116, 137, 159, and 175
16.25 A sample of 400 high-reliability switches was placed on a life test until the first five failures occurred and the test was then terminated. The first five failures were at 268, 395, 479, 685 and 964 hours. Find a 99% lower confidence limit for the mean life of the switches assuming an
16.24 Twenty motors are put on an accelerated life test without replacement and the test is truncated after 5 failures. If the first 5 failures occurred at 12.5, 16.8, 24.3, 27.6 and 32.1 hours, assuming an exponential model, (a) determine a 95% confidence interval for the failure rate of such
16.23 A transmitter has an exponential life distribution with a failure rate of α = 0.00025 failures per hour. (a) What is the probability that the transmitter will fail during the first 400 hours it is in operation? (b) What is the probability that three such transmitters will all survive the
16.22 A system consists of 7 identical components connected in parallel. Determine the reliability of each component if the overall reliability of the system is to be 0.90?
16.21 Derive the formula for the variance of the Weibull distribution given on page 514.
16.20 Show that the reliability function associated with the Weibull failure-time distribution is given by R(t) = e−α t β
16.19 Using the estimates of the parameters of the Weibull model obtained in Exercise 16.18, estimate the probability that this kind of diaphragm valve will perform satisfactorily for at least 150 hours.
16.18 A sample of 60 diaphragm valves, used in the control system of a chemical process, are placed on life test without replacement. The first 9 failures are observed after 3.6 6.9 9.5 15.7 27.3 41.2 81.7 178.3 227.1 hours. Using the Weibull model, estimate the mean life of this valve. How does
16.17 A sample of 450 bulbs was placed on a life test consisting of repeated on-off cycles. The test was terminated after the fifth failure. The first five failure times were 469, 724, 862, 995 and 1,246. Find a 99% lower confidence limit for the mean life, in number of cycles, of the bulbs. Use
16.16 One hundred devices are put on life test and the times to failure (in hours) of the first 10 that fail are 7.0 14.1 18.9 31.6 52.8 80.0 164.5 355.4 451.0 795.1 Assuming a Weibull failure-time distribution, estimate the parameters α and β as well as the failure rate at 1,000 hours. How does
16.15 Using the fact that 2 Tr /μ is a value of a random variable having the chi square distribution with 2 r degrees of freedom, derive the confidence interval for μ given on page 511.
16.14 In life testing, we are sometimes interested in establishing tolerance limits for the life of a component (see Section 15.7); in particular, we may be interested in a one-sided tolerance limit t ∗, for which we can assert with a (1 − α)100% confidence that at least 100 · P percent of
16.13 To investigate the average time to failure of a certain soldered object subject to continuous flow of current, 5 soldered objects were subjected to specified volts and amperes of current and their times to failure were 426, 589, 694, 810 and 1,100 circuits of current. (a) Assuming the
16.12 With reference to the data in Exercise 16.11, make a total time on test plot.
16.11 In a nonreplacement life test, 50 water turbines were put into continuous operation, and the first 3 failures occurred after 400, 600, and 1,050 hours. (a) Assuming the exponential model, construct an 85% confidence interval for the mean life of this kind of water turbines. (b) To check the
16.10 Suppose that 75 units are put on a life test, each unit that fails is immediately replaced, and the test is discontinued after 10 units have failed. If the tenth failure occurred at 850 hours, assuming an exponential model, (a) construct a 99% confidence interval for the mean life of such
16.9 If the spare part of a cement mixer has the Weibull failure-time distribution with the parameters α = 0.001 per hour and β = 0.65, find the probability that it will not operate successfully for at least 1,000 hours.
16.8 After installation, the lifetime of a ball bearing is modeled as an exponential distribution with failure rate α = 0.001 failures per day. (a) What is the probability that the ball bearing will fail within the first 90 days of installation? (b) What is the probability that three such ball
16.7 A transistor has a constant failure rate of 0.005 per ten thousand hours. (a) What is the probability that it will perform satisfactorily for at least 75,000 hours?(b) What is the 20,000-hour reliability of a chip consisting of 6 such transistors connected in series?
16.6 As indicated in the text, one often distinguishes between initial failures, random failures during the useful life of the product, and wear-out failures. For a given product, suppose the probability of an initial failure (a failure prior to time t = α) is θ1, the probability of a wear-out
16.5 In some reliability problems we are concerned only with initial failures, treating a component as if (for all practical purposes) it never fails, once it has survived past a certain time t = α. In a problem like this, it may be reasonable to use the failure rate Z(t) = ⎧ ⎪⎨ ⎪⎩ β
16.4 Suppose that a machine’s operation is regarded as a system having three main components: A (team), B (power supply), andC (assembly). Suppose, furthermore, that component A can be regarded as a parallel subsystem consisting of A1 (worker), A2 (supervisor), and A3 (operations manager); and C
16.3 A system consists of 6 components connected as in Figure 16.3. Find the overall reliability of the system, given that the reliabilities of A, B,C, D, E, and F are, respectively, 0.95, 0.80, 0.90, 0.99, 0.90, and 0.85. A B C D E F
16.2 A system consists of 5 identical components connected in parallel. Determine the reliability of each component if the overall reliability of the system is to be 0.96?
16.1 An electric circuit consists of 7 transistors connected in parallel. Determine the reliability of each transistor if the overall reliability of the circuit is to be 0.99.
15.28 The following are the number of pounds per day shipped by a trucking company. 222,415 140,670 396,868 240,678 101,786 166,217 177,900 349,900 131,100 465,800 417,700 305,600 264,500 224,400 360,400 211,600 378,200 285,400 166,100 230,900 593,300 214,200 147,800 119,510 159,200 353,200 408,300
15.27 A critical width dimension on an integrated circuit board was measured on 100 boards. The ordered measurements are: 2.500 2.502 2.502 2.502 2.503 2.503 2.503 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.504 2.505 2.505 2.505 2.505 2.505 2.505
15.26 Explain, from the perspective of quality improvement programs, why the x, R, and fraction defective charts should be used to listen to the process and observe its natural variability, at any stage, rather than for the long-run control of the process.
15.25 With reference to Example 4. (a) verify the calculation of the tolerance bound L; (b) if the confidence is decreased to 90%, calculate the new tolerance bound (use K = 2.010); (c) check the cardboard strength data for departures from normality using a normal-score plot.
15.24 With reference to the discussion on page 492, calculate the CUSUM using 2.25 in place of 2.00 as the centering value. Also make the CUSUM chart.
15.23 With reference to the interrequest time data on page 29, obtain 95% tolerance limits on the proportion P = 0.90 of the population of interrequest times. Take logs, use the normal theory approach, and then transform back to the original scale.
15.22 With reference to the aluminum alloy strength data on page 29, obtain two-sided 95% tolerance limits on the proportion P = 0.90 of the population of strengths.
15.21 A process for the manufacture of film has performed in the past with an average of 0.8 imperfections per 10 linear feet. (a) Construct a chart to be used in the inspection of 10-foot sections. (b) Discuss the control if 20 successive 10-foot sections contained, respectively, 1, 0, 0, 1, 3, 1,

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