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statistics principles and methods

Questions and Answers of Statistics Principles And Methods

For the following probability mass function:(a) Compute the expected value of X, (b) compute the variance and standard deviation, (c) compute the probability that X ≥ 4. x 0 1 2 3 4 5 6 0.05 0.25
For the probability mass function of Problem 3.15, determine the following probabilities: (a) P(X =4); (b) P(X = 5); (c) P(X ≤ 5); (d) P(X < 5); (e) P(4 < X ≤ 7); and (f) P(X ≥ 7).
Given the following probability mass function:determine the value of i that results in a legitimate mass function. Graph both the probability and cumulative mass functions. Px(x) for 0 x-1 x-2 x-3
Given the following probability mass function:determine the value of i that results in a legitimate mass function. Graph both the probability and cumulative mass functions. x=1 2i x-2 Px (x)- for 3i
Given the following cumulative mass function, derive the mass function:Graph both the probability and cumulative mass functions. [0.2 x-2 0.2 x-3 0.2 x-4 0.5 x-5 Fx(x) - for 0.7 x-6 0.8 x-7 0.9 x-8
An automobile insurance company classifies insured drivers as low risk (L), medium risk (M), and high risk (H). The population of insured drivers is characterized from the company records to have the
An electronic device is operated under three temperature settings of low, medium, and high (i.e., L, M, H) and two vibration conditions of V1 and V2. The reliability of the device depends on the
A construction site receives fill material from three sources, with sources A, B, and C providing 15, 25, and 60% of the total, respectively. On the average, fill material from sources A, B, and C do
Find the following conditional probabilities:a. On a single roll of a die, the probability of a 3 given that the value is an odd integer (draw the sample space for the conditional event)b. The
A shipping company facilitates for customers the transfer of any items from any location to another within the United States. The company transfers 20, 50, and 30% of the items by air, ground, and
A pressure vessel has five pressure relief valves. The probability that a valve will operate on demand is 0.75. What is the probability that at least one valve will operate on demand? What is the
An anti-missile defense system has a 99% probability of detection of an incoming missile, that is and a 0.1% false detection probability, that is, the probability of detecting an incoming missile
A weld inspection method has a 90% probability of detection of a defect in a welded joint that contacts such a defect, and a 5% false detection probability, that is, the probability of detecting a
Baggage screening equipment has a 99% probability of detection of a prohibited item in a bag that contains such an item, and a false detection probability, that is, the probability of detecting a
Materials for a construction site are supplied by two sources A and B. Upon arrival of all materials from both sources, the construction is started after the arrival of workers. If the probability
A highway owned and managed by a local authority is maintained by dividing it into ten segments separated at identified stations. Each segment is inspected every year and given a pavement rating of
A concrete beam may fail by shear or flexure. The failure probability in shear is equal to failure probability in flexure, and the probability of failure in shear when the beam is loaded beyond its
A concrete beam may fail by shear or flexure. The failure probability in shear is 0.01, and the failure probability in flexure is 0.05 for the following cases: (1) the failure events in shear and
Two loads A and B are applied on a structural column and are mutually exclusive. The probability that the beam is safe against load A is 0.7 and against load B is 0.9. What is the probability that
The perimeter security system of a critical facility consists of five nested security zones, that is, an intruder must pass through the first zone successfully before encountering the second zone,
The quality control of an electronic device requires the examination of its performance experimentally using five temperature settings, three humidity levels, and six vibration conditions. How many
A rocket consists of 10 subsystems. Each subsystem operates as intended or does not operate as intended upon demand. Upon demand, i.e., firing the rocket, the rocket could malfunction due to the
A manufacturer produced 30 identical cellular devices that were shipped to selected clients for beta testing. The manufacturer suspected that the devices might have a defect, and decided to recall 10
A manufacturer produced 10 identical cellular devices that were shipped to selected clients for beta testing. The manufacturer suspected that the devices might have a defect, and decided to recall 2
The scores on a test were distributed as shown below for a class of 60 students. Convert the frequency histogram to a probability distribution. What is the probability that a student had a score of
What is the difference between the population and a sample? A construction engineer obtains five specimens of steel reinforcing bars from a shipment to a construction site. What is the corresponding
Construct a Venn diagram for a deck of playing cards (four suits, 13 cards per suit). Show the following events:a. A = all diamonds and all acesb. B = all face cardsc. C = the intersection of red
The traffic that makes a left turn at an intersection consists of two types of vehicles, types A and B.A type A vehicle is twice the length of type B. The left-turn lane can accommodate eight
For the data and events of Problem 3.2, sketch the following events: A∪ B, A∩ B, C ∪ D, C ∩ D, A ∪ C, A(BC), A, and A∩ B.
Construct Venn diagrams for each of the following:a. Deck of playing cardsb. Roll of a diec. Letter grades on a test, assuming equal probabilities for each graded. Letter grades on a test, assuming
A construction tower crane can operate up to a height H of 300 ft, a range (radius) R of 50 ft, and an angle ϕ of ±90° in a horizontal plane. Sketch the sample space of operation of the crane.
A construction manager needs to procure building materials for the construction of a bridge. The following sources are identified:Define the sample space of all possible combinations of sources
On a monthly basis, accidents were occurring at two intersections (A and B) at similar rates. Traffic control measures were taken at one of the two intersections (A), and then monthly accidents were
Using the data of Problem 2.41, construct box-and-whisker plots for the 1920–59 and 1960–99 periods.
Create a box-and-whisker plot of the data in Problem 2.33. Also create a relative frequency histogram of the data. Discuss and compare the information content of the two graphical analyses.
If the length of an object (x) is recorded in units of feet and the measurements are transformed to units of meters (y), values of the mean, standard deviation, and variance will change by what
Equation 2.7 provides the definition of the variance. Equation 2.8 is more commonly used to compute a sample variance than Equation 2.7. Derive Equation 2.8 from Equation 2.7.
For the data of Problem 2.33, determine the dispersion measures: the variance, standard deviation, and COV.
For the data of Problem 2.27, determine the dispersion measures: the variance, standard deviation, and COV.
For the data of Problem 2.26, determine the dispersion measures: the variance, standard deviation, and COV.
The winner’s shares ($ × 103, not corrected for inflation) of the purse for the Kentucky Derby from 1920 to 1999, by decade, are as follows:Compute the mean, standard deviation, and COV for each
Using the data of Problem 2.49, compute the mean, standard deviation, and COV for the accident rate at intersection B.
The calculation of the mean in Equation 2.5 uses the formula in Equation 2.4. Develop a formula for computing the mean for the calculations of Equation 2.6.
Two sections of a class are given a quiz, which has a total of 10 1-point questions. The distributions of the grades are as follows:Compute the mean, median, and mode of the grades for each section.
If a small sample of engineering measurements contains one extreme event, compare the use of the average and median values as measures of central tendancy. Illustrate your general point with the
For the data of Problem 2.33, determine the central tendency measures: the average value, median, and mode.
For the data of Problem 2.27, determine the central tendency measures: the average value, median, and mode.
For the data of Problem 2.26, determine the central tendency measures: the average value, median, and mode.
The following data are the maximum daily ozone concentrations for the months indicated. Graph the data in a way that will emphasize the monthly variation in the concentration. Also, graph the data in
Using all of the data of Problem 2.41, construct histograms with cell widths of (a) 100 and (b) 50. What general observation can be made from a comparison of the two histograms?
Figure 2.23 compares the relative frequency histograms for assumed and simulated data. The two do not agree exactly. Propose a means of deciding how large a sample of simulated data would be needed
Two laboratories are each given 30 samples over the course of a year to measure the concentration of a pollutant that has a known concentration of 250 ppb. Form histograms of the measured
Following are scores on a test in the form of ranges, with the corresponding number of students in parentheses: 55–60 (2); 60–65 (4); 65–70 (7); 70–75 (7); 75–80 (1); 80–85 (6); 85–90
An electronic board will be mass produced using a newly developed manufacturing process. The process was tested by producing 20 products, and the number of defects was counted on each board.The
Piles are commonly used in foundations of civil work structures. Test piles were driven and used to measure pile strength at a selected site. The following strength data (in kips) were
The following concrete strength data (in ksi) were collected using an ultrasonic nondestructive testing method at different locations of an existing structure: 3.5, 3.2, 3.1, 3.5, 3.6, 3.2, 3.4, 2.9,
Construct a histogram of the simulated discharge data of Table 2.5 using an interval of 40 cms.Discuss the distribution of discharges suggested by the histogram. Compare the histogram with Figure
Construct a histogram of the discharge data of Table 2.3 using a 25-cms interval. Compare the shape of the histogram with that of Figure 2.21. Discuss the differences noted.
Construct a histogram of the river stage data of Table 2.3 using a 0.5-m interval. Compare the shape of the histogram of Figure 2.21. Discuss any differences noted.
Using the bridge data in Problem 2.15, show the number of bridges as a function of year and by bridge type using a line chart, a pie chart, and three-dimensional surface chart.
A local highway department compiled the following percentages from accident records according to traffic-control method (flashing red light, two-way stop signs, or four-way stop signs) and accident
The following data give the age distribution of U.S. citizens as a function of age group. Select a method for graphing the results. Interpret the results. Then combine the values into three
For the eight methods of graphical analysis given in Section 2.3, develop a classification system for distinguishing among them. The classification system should center on basic, yet important,
The following percentages indicate the change in rural, suburban, and central city U.S. populations from 1900 to 1970. Present the data graphically to emphasize the decline in the proportion of the
The quadratic polynomial is commonly used to relate two variables, y and x, such that the relationship is nonlinear. An oceanographer measures light depth penetration in an estuary (y, microamps×
The power model y = axb is widely used in engineering. (a) Develop line graphs for a = 1 and b = {0.5, 1.0, 1.5} for 0 ≤ x ≤ 2. (b) Develop line graphs for b = 0.5 and a = {0.5, 1.0, 1.5} for 0
Plot the data shown in the following table using a column chart: Number of Constructed Bridges by Year Superstructure Type 1989 1990 1991 Steel 5 10 12 Concrete Prestressed concrete 14 10 6 6 275
Obtain data on the winning time of the Belmont Stakes. Separate the data into time groups and present the percentage in a column chart.
Create column charts to present the following estimates of U.S. production of bituminous and lignite coal from surface and underground mines:Use one column chart to emphasize the temporal variation
Compare the graphical analyses of Figures 2.3, 2.5a, and 2.5b, and identify the circumstances under which each would be the most appropriate for making decisions.
Create a bar chart to display the following data, which provide the estimated remaining strippable resources and reserves of bituminous coal in the United States (billions of short tons): Alaska 0.9
Obtain data on the winning time of the Kentucky Derby from 1919 to the present. Separate the data into time groups and graph the data as a pie chart, which shows the percentage in each time group.
Obtain data on U.S. family size (i.e., 2 people, 3 people, etc.) and create a pie chart that shows the percentage in each size group.
For years in different decades (e.g., 1970, 1980, 1990, 2000) obtain data on the source of petroleum imports into the United States based on region (e.g., South America, Saudi Arabia, Canada, etc.)
Obtain data on the percent forested for regions of the United States (e.g., South, Central, Mid-Atlantic, New England, etc.). Present the percent of the total forested area in a pie chart.
The following data are the solid waste (millions of tons) produced annually in the United States:Construct a pie chart to present the data. Discuss the merits of presenting the data in a pie chart
Using the data of Problem 2.18 construct an area chart and a column chart if the population of the United States is 295 million. Discuss the merits of the alternative figures.
Using the data from Problem 2.18 and the following population totals, construct an area chart that shows the total and the breakdown of the total population in rural, suburban, and central city. Year
Using the copper content of steel as a variable of interest, identify a function that would be measured for each of the four measurement scales.
Using age as a variable of interest, identify a function that would be measured on each of the scales:nominal, ordinal, interval, and ratio.
For each of the measurement scales, identify five variables that are measured with the scale.
Use the rand function in a spreadsheet to randomly generate 100 random numbers, and use linear transformation to produce random values in the range [–15, 325].
Use the rand function in a spreadsheet to randomly generate 100 random numbers, and use linear transformation to produce random values in the range [–5, 5].
Use the rand function in a spreadsheet to randomly generate 100 random numbers, and use linear transformation to produce random values in the range [22, 132].
Use the rand function in a spreadsheet to randomly generate 20 random numbers, and use linear transformation to produce random values in the range [2, 6].
Use the rand function in a spreadsheet to randomly generate 20 random numbers. Repeat the process for another 20 random numbers. Is the first set of random numbers the same as the second set?
Use the midsquare method to generate 20 random numbers using a seed of 2468.
Use the midsquare method to generate 20 random numbers using a seed of 9658.
Use the midsquare method to generate 10 random numbers using a seed of 8371.
Use the midsquare method to generate 10 random numbers using a seed of 3456.
The probabilities of the largest magnitude of an earthquake in any decade are as follows:Construct a transformation graph that could transform a random number (E) over the range from 0 to 1 to the
Assume the value of X is random and can take on values from 0 to 1. Assume the following transformation graph relates X to the annual number of fatal accidents (N) at an intersection:A random-number
Develop a transformation graph for producing a computer chip by a factory that has a 1/1000 defective-chip probability.
Develop a transformation graph for flipping a thumbtack that has a 2/3 probability for its needle pointing down.
Show the transformation graph that transforms the roll of a die (W) to the value of the flip of an unfair coin (C) for which the probability of a tail is 5/6.
Show the development of the probability graph P(Z) versus Z given in Section 1.3.2.
Provide examples of ignorance types provided in Figure 1.1.
Provide examples of aleatory and epistemic uncertainty for an engineered system. Discuss the differences.How can you reduce uncertainty for each type?
Select an engineering system for which you can define different levels of abstractions on the system with different abstraction aspects. Identify the abstracted aspects of the system, the
It has been known for some time that men with older brothers are more likely to be homosexual than men without older brothers. One explanation for this effect has been that this is a phenomenon of

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