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applied statistics and probability for engineers

Questions and Answers of Applied Statistics And Probability For Engineers

In 1879, A. A. Michelson made 100 determinations of the velocity of light in air using a modification of a method proposed by the French physicist Foucault. He made the measurements in five trials of
Transformations. In some data sets, a transformation by some mathematical function applied to the original data, such as or log y, can result in data that are simpler to work with statistically than
Based on the plot, what tentative conclusions can you draw?
Construct a normal probability plot of the effluent discharge temperature data from Exercise
Construct normal probability plots for two groups of the data: the first 40 and the last 40 observations. Construct both plots on the same axes.What tentative conclusions can you draw?
Reconsider the data in Exercise
A communication channel is being monitored by recording the number of errors in a string of 1000 bits. Data for 20 of these strings follow:Read data across.3 1 0 1 3 2 4 1 3 1 1 1 2 3 3 2 0 2 0 1(a)
Prepare comparative box plots for two groups of observations: the first 40 and the last 40. Comment on the information in the box plots.
Reconsider the data from Exercise
Plot the data for female and male students on the same axes. Does height seem to be normally distributed for either group of students? If both populations have the same variance, the two normal
Construct two normal probability plots for the height data in Exercises 6-22 and
Does it seem reasonable to assume that the concentration of suspended solids in water from this particular lake is normally distributed?
Construct a normal probability plot of the suspended solids concentration data in Exercise
Does it seem reasonable to assume that this variable is normally distributed?
Construct a normal probability plot of the wine quality rating data in Exercise
Does it seem reasonable to assume that cycles to failure is normally distributed?
Construct a normal probability plot of the cycles to failure data in Exercise
Does it seem reasonable to assume that octane rating is normally distributed?
Construct a normal probability plot of the octane rating data in Exercise
Does it seem reasonable to assume that O-ring joint temperature is normally distributed?Discuss any interesting features that you see on the plot.
Construct a normal probability plot of the O-ring joint temperature data in Exercise
Does it seem reasonable to assume that visual accommodation is normally distributed?
Construct a normal probability plot of the visual accommodation data in Exercise
Does it seem reasonable to assume that breakdown time is normally distributed?
Construct a normal probability plot of the insulating fluid breakdown time data in Exercise
Does it seem reasonable to assume that piston ring diameter is normally distributed?
Construct a normal probability plot of the piston ring diameter data in Exercise
Their analysis requires some advanced knowledge of statistics and statistical model building.) (read down, then left to right)(a) Construct a time series plot of these data.(b) Construct and
Construct and interpret either a digidot plot or a stemand-leaf plot of these data. The 100 annual Wolfer sunspot numbers from 1770 to 1869 follow. (For an interesting analysis and interpretation of
The College of Engineering and Applied Science at Arizona State University had a VAX computer system.Response times for 20 consecutive jobs were recorded and are as follows: (read across)Construct
In Exercise 6-44, data was presented on the cold start ignition time of a particular gasoline used in a test vehicle. A second formulation of the gasoline was tested in the same vehicle, with the
Use the data on heights of female and male engineering students from Exercises 6-22 and 6-29 to construct comparative box plots. Write an interpretation of the information that you see in these plots.
Reconsider the wine rating data in Exercise 6-27..Construct a box plot of the wine ratings and write an interpretation of the plot. How does the box plot compare in interpretive value to the original
Construct a box plot of the yardage distance and write an interpretation of the plot. How does the box plot compare in interpretive value to the original stem-and-leaf diagram in Exercise 6-25?
Reconsider the golf ball overall distance data in Exercise
Reconsider the water quality data in Exercise 6-24..Construct a box plot of the concentrations and write an interpretation of the plot. How does the box plot compare in interpretive value to the
Reconsider the female engineering student height data in Exercise 6-22.. Construct a box plot of the heights and write an interpretation of the plot. How does the box plot compare in interpretive
Construct a box plot of the strengths and write an interpretation of the plot. How does the box plot compare in interpretive value to the original stem-and-leaf diagram in Exercise 6-23?
Reconsider the spot weld shear strength data in Exercise
Reconsider the motor fuel octane rating data in Exercise 6-14.. Construct a box plot of the yardages and write an interpretation of the plot. How does the box plot compare in interpretive value to
Reconsider the golf course yardage data in Exercise 6-3.Construct a box plot of the yardages and write an interpretation of the plot.
The following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days:43 47 51 48 52 50 46 49 45 52 46 51 44 49 46 51 49 45 44 50 48 50 49 50 (a)
Exercise 6-12 presents drag coefficients for the NASA 0012 airfoil. You were asked to calculate the sample mean, sample variance, and sample standard deviation of those coefficients.(a) Find the
The nine measurements that follow are furnace temperatures recorded on successive batches in a semiconductor manufacturing process (units are ): 953, 950, 948, 955, 951, 949, 957, 954, 955.(a)
The “cold start ignition time” of an automobile engine is being investigated by a gasoline manufacturer. The following times (in seconds) were obtained for a test vehicle: 1.75, 1.92, 2.62, 2.35,
An article in the Transactions of the Institution of Chemical Engineers (Vol. 34, 1956, pp. 280–293) reported data from an experiment investigating the effect of several 31 F2 process variables on
Exercise 6-13 presented the joint temperatures of the O-rings (°F) for each test firing or actual launch of the space shuttle rocket motor. In that exercise you were asked to find the sample mean
The Pareto Chart. An important variation of a histogram for categorical data is the Pareto chart. This chart is widely used in quality improvement efforts, and the categories usually represent
Construct a histogram for the pinot noir wine rating data in Exercise 6-27.. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display?
Construct a histogram for the semiconductor speed data in Exercise 6-26.. Comment on the shape of the histogram.Does it convey the same information as the stem-andleaf display?
Construct a histogram with 10 bins for the overall distance data in Exercise 6-25.. Comment on the shape of the histogram.Does it convey the same information as the stem-andleaf display?
Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display?
Construct a histogram for the water quality data in Exercise
Construct a histogram with 10 bins for the spot weld shear strength data in Exercise 6-23.. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf display?
Construct a histogram for the female student height data in Exercise 6-22..
Do both histograms display similar information?
Construct a frequency distribution and histogram with 16 bins for the motor fuel octane data in Exercise 6-14.. Compare its shape with that of the histogram with eight bins from Exercise
Construct a frequency distribution and histogram for the yield data in Exercise 6-17..
Construct a frequency distribution and histogram for the cotton content data in Exercise 6-16..
Construct a frequency distribution and histogram using the failure data from Exercise 6-15..
Construct a frequency distribution and histogram for the motor fuel octane data from Exercise 6-14.. Use eight bins.
A Comparative Stem-and-Leaf Diagram. In Exercise 6-22, we presented height data that was self-reported by female undergraduate engineering students in a core course at ASU. In the same class, the
In their book Introduction to Linear Regression Analysis (3rd edition, Wiley, 2001) Montgomery, Peck, and Vining present measurements on NbOCl3 concentration from a tube-flow reactor experiment. The
A group of wine enthusiasts taste-tested a pinot noir wine from Oregon. The evaluation was to grade the wine on a 0 to 100 point scale. The results follow:distance test is conducted by hitting balls
A semiconductor manufacturer produces devices used as central processing units in personal computers. The speed of the device (in megahertz) is important because it determines the price that the
The United States Golf Association tests golf balls to ensure that they conform to the rules of golf. Balls are tested for weight, diameter, roundness, and overall distance. The overall distance test
An important quality characteristic of water is the concentration of suspended solid material. Following are 60 measurements on suspended solids from a certain lake. Construct a stem-and-leaf diagram
The shear strengths of 100 spot welds in a titanium alloy follow. Construct a stem-and-leaf diagram for the weld strength data and comment on any important features that you notice. 5408 5431 5475
The female students in an undergraduate engineering core course at ASU self-reported their heights to the nearest inch. The data are 62 64 66 67 65 68 61 65 67 65 64 63 67 68 64 66 68 69 65 67 62 66
Find the median and the quartiles for the yield data in Exercise 6-19.
Explain how these three measures of location describe different features in the data.
Find the median, mode, and sample average of the data in Exercise
Find the median and the quartiles for the failure data in Exercise 6-15.
Find the median and the quartiles for the motor fuel octane data in Exercise 6-14.
The following data represent the yield on 90 consecutive batches of ceramic substrate to which a metal coating has been applied by a vapor-deposition process. Construct a stemand-leaf display for
The percentage of cotton in material used to manufacture men’s shirts follows. Construct a stem-and-leaf display for the data. 34.2 37.8 33.6 32.6 33.8 35.8 34.7 34.6 33.1 36.6 34.7 33.1 34.2 37.6
The following data are the numbers of cycles to failure of aluminum test coupons subjected to repeated alternating stress at 21,000 psi, 18 cycles per second:(a) Construct a stem-and-leaf display for
An article in Technometrics (Vol. 19, 1977, p. 425)presents the following data on the motor fuel octane ratings of several blends of gasoline:Construct a stem-and-leaf display for these data. 88.5
The following data are the joint temperatures of the O-rings (°F) for each test firing or actual launch of the space shuttle rocket motor (from Presidential Commission on the Space Shuttle
An article in the Journal of Aircraft (1988) describes the computation of drag coefficients for the NASA 0012 airfoil.Different computational algorithms were used at with the following results (drag
The pH of a solution is measured eight times by one operator using the same instrument. She obtains the following data: 7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.16, and 7.18.(a) Calculate the sample
Exercise 6-5 describes data from an article in Human Factors on visual accommodation from an experiment involving a high-resolution CRT screen.(a) Construct a dot diagram of this data.(b) Data from a
Consider the solar intensity data in Exercise 6-6.Prepare a dot diagram of this data. Indicate where the sample mean falls on this diagram. Give a practical interpretation of the sample mean.
Preventing fatigue crack propagation in aircraft structures is an important element of aircraft safety. An engineering study to investigate fatigue crack in n 9 cyclically loaded wing boxes
The April 22, 1991 issue of Aviation Week and Space Technology reports that during Operation Desert Storm, U.S.Air Force F-117A pilots flew 1270 combat sorties for a total of 6905 hours. What is the
The following data are direct solar intensity measurements(watts/m2) on different days at a location in southern Spain: 562, 869, 708, 775, 775, 704, 809, 856, 655, 806, 878, 909, 918, 558, 768, 870,
An article in Human Factors (June 1989) presented data on visual accommodation (a function of eye movement)when recognizing a speckle pattern on a high-resolution CRT screen. The data are as follows:
An article in the Journal of Structural Engineering(Vol. 115, 1989) describes an experiment to test the yield strength of circular tubes with caps welded to the ends. The first yields (in kN) are 96,
The January 1990 issue of Arizona Trend contains a supplement describing the 12 “best” golf courses in the state.The yardages (lengths) of these courses are as follows: 6981, 7099, 6930, 6992,
In Applied Life Data Analysis (Wiley, 1982), Wayne Nelson presents the breakdown time of an insulating fluid between electrodes at 34 kV. The times, in minutes, are as follows:0.19, 0.78, 0.96, 1.31,
Eight measurements were made on the inside diameter of forged piston rings used in an automobile engine. The data(in millimeters) are 74.001, 74.003, 74.015, 74.000, 74.005, 74.002, 74.005, and
Suppose that the range of the continuous variables X and Y is 0 x a and 0 y b. Also suppose that the joint probability density function fXY (x, y) g(x)h( y), where g(x) is a function only of
Suppose that the joint probability function of the continuous random variables X and Y is constant on the rectangle 0 x a, 0 y b. Show that X and Y are independent.
Show that if X1, X2, p , Xp are independent random variables and Y c1X1 c2X2 cpXp,You can assume that the random variables are continuous. V(Y) = c{V(X) + cV(X2) + + cV(Xp)
Show that if X1, X2, p , Xp are independent, continuous random variables, P(X1 A1, X2 A2, p , Xp Ap) P(X1 A1)P(X2 A2) p P(Xp Ap) for any regions A1, A2, p , Ap in the range of X1, X2, p
A small company is to decide what investments to use for cash generated from operations. Each investment has a mean and standard deviation associated with the percentage gain. The first security has
The permeability of a membrane used as a moisture barrier in a biological application depends on the thickness of three integrated layers. Layers 1, 2, and 3 are normally distributed with means of
The permeability of a membrane used as a moisture barrier in a biological application depends on the thickness of two integrated layers. The layers are normally distributed with means of 0.5 and 1
A mechanical assembly used in an automobile engine contains four major components. The weights of the components are independent and normally distributed with the following means and standard
The time for an automated system in a warehouse to locate a part is normally distributed with a mean of 45 seconds and a standard deviation of 30 seconds. Suppose that independent requests are made

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