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Questions and Answers of Statistics

The width of a casing for a door is normally distributed with a mean of 24 inches and a standard deviation of 1/8 inch. The width of a door is normally distributed with a mean of 23 and 7/8 inches
A U-shaped component is to be formed from the three parts A, B, and C. The picture is shown in Fig. 5-20. The length of A is normally distributed with a mean of 10 millimeters and a standard
Soft-drink cans are filled by an automated filling machine and the standard deviation is 0.5 fluid ounces assume that the fill volumes of the cans are independent, normal random variables.(a) What is
The photo resist thickness in semiconductor manufacturing has a mean of 10 micrometers and a standard deviation of 1 micrometer. Assume that the thickness is normally distributed and that the
Assume that the weights of individuals are independent and normally distributed with a mean of 160 pounds and a standard deviation of 30 pounds. Suppose that 25 people squeeze into an elevator that
Show that the following function satisfies the properties of a joint probability mass function:
Continuation of Exercise 5-96. Determine the following probabilities:(a) P(X < 0.5, Y < 1.5)(b) P(X < 1)(c) P(X < 1.5)(d) P(X > 0.5, Y < 1.5)(e) Determine E(X), E(Y), V(X), and V(Y).
Continuation of Exercise 5-96. Determine the following:(a) Marginal probability distribution of the random variable X(b) Conditional probability distribution of Y given that X = 1(c) E(Y|X = 1)(d)
The percentages of people given an antirheumatoid medication who suffer severe moderate or minor side effects are 10, 20, and 70%, respectively. Assume that people react independently and that 20
The back off torque required to remove bolts in a steel plate is rated as high, moderate, or low. Historically, the probability of a high, moderate, or low rating is 0.6, 0.3, or 0.1, respectively.
Continuation of Exercise 5-100(a) What is the conditional distribution of the number of bolts rated low given that 16 bolts are rated high?(b) What is the conditional expected number of bolts rated
To evaluate the technical support from a computer manufacturer, the number of rings before a call is answered by a service representative is tracked. Historically, 70% of the calls are answered in
Continuation of Exercise 5-102(a) What is the conditional distribution of the number of calls requiring five rings or more given that eight calls are answered in two rings or less?(b) What is the
Determine the value of c such that the function f (x, y) = cx2y for 0 < x < 3 and 0 < y < 2 satisfies the properties of a joint probability density function.
Continuation of Exercise 5-104. Determine the following:(a) P(X < 1, Y < 1)(b) P(X < 2.5)(c) P(1 < Y < 2.5)(d) P(X > 2, 1 < Y < 1.5)(e) E(X)(f) E(Y)
Continuation of Exercise 5-104.(a) Determine the marginal probability distribution of the random variable X.(b) Determine the conditional probability distribution of Y given that X = 1.(c) Determine
The joint distribution of the continuous random variables X, Y, and Z is constant over the region(a) Determine P(X2 + Y2 < 0.5)(b) Determine P(X2 + Y2 < 0.5, Z < 2)(c) What is the joint conditional
Continuation of Exercise 5-107.(a) Determine the conditional mean of Z given that X = 0 and Y = 0.(b) In general, determine the conditional mean of Z given that X = x and Y = y.
Suppose that X and Y are independent, continuous uniform random variables for 0 < x < 1 and 0 < y < 1. Use the joint probability density function to determine the probability that
The lifetimes of six major components in a copier are independent exponential random variables with means of 8000, 10,000, 10,000, 20,000, 20,000, and 25,000 hours, respectively. (a) What is the
Contamination problems in semiconductor manufacturing can result in a functional defect, a minor defect, or no defect in the final product. Suppose that 20, 50, and 30% of the contamination problems
The weight of adobe bricks for construction is normally distributed with a mean of 3 pounds and a standard deviation of 0.25 pound. Assume that the weights of the bricks are independent and that a
The length and width of panels used for interior doors (in inches) are denoted as X and Y, respectively. Suppose that X and Y are independent, continuous uniform random variables for 17.75 < x <
The weight of a small candy is normally distributed with a mean of 0.1 ounce and a standard deviation of 0.01 ounce. Suppose that 16 candies are placed in a package and that the weights are
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
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
Suppose X and Y have a bivariate normal distribution with σX = 4 σY = 1μ = 4, μY =4, and. p = - 2.0 Draw a rough contour plot of the joint probability density function.
IfDetermine E(X), E(Y), V(X), V(Y), and p by recorganizing the parameters in the joint probability density function.
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
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
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
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
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,
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,
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
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
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,
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
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
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.
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
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
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 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 Techno metrics (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.
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
The percentage of cotton in material used to manufacture men€™s shirts follows. Construct a stem-and-leaf display for the data.
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 stem and-leaf display for
Find the median and the quartiles for the motor fuel octane data in Exercise 6-14.
Find the median and the quartiles for the failure data in Exercise 6-15.
Find the median, mode, and sample average of the data in Exercise 6-16. Explain how these three measures of location describe different features in the data.
Find the median and the quartiles for the yield data in Exercise 6-19.
The female students in an undergraduate engineering core course at ASU self-reported their heights to the nearest inch. The data are(a) Calculate the sample mean and standard deviation of height.(b)
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.
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 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
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
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:(a) Construct a stem-and-leaf diagram for
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 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 male
Construct a frequency distribution and histogram for the motor fuel octane data from Exercise 6-14. Use eight bins.
Construct a frequency distribution and histogram using the failure data from Exercise 6-15.
Construct a frequency distribution and histogram for the cotton content data in Exercise 6-16.
Construct a frequency distribution and histogram for the yield data in Exercise 6-17.
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 6-30. Do both
Construct a histogram for the female student height data in Exercise 6-22.
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 water quality data in Exercise 6-24. Comment on the shape of the histogram. Does it convey the same information as the stem-and-leaf 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-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-and leaf display?
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?
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
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
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
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,
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)
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 following data are the temperatures of effluent at discharge from a sewage treatment facility on consecutive days:(a) Calculate the sample mean and median.(b) Calculate the sample variance and
Reconsider the golf course yardage data in Exercise 6-3. Construct a box plot of the yardages and write an interpretation of the plot.
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 the
Reconsider the spot weld shear strength data in Exercise 6-23. Construct a box plot of the strengths and write an interpretation of the plot. How does the box plot compare in interpretive value to
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
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 golf ball overall distance data in Exercise 6-25. Construct a box plot of the yardage distance and write an interpretation of the plot. How does the box plot compare in interpretive
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
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.
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
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
The following data are the viscosity measurements for a chemical product observed hourly (read down, then left to right).(a) Construct and interpret either a digidot plot or a separate stem-and-leaf
The pull-off force for a connector is measured in a laboratory test. Data for 40 test specimens follow (read down, then left to right).(a) Construct a time series plot of the data.(b) Construct and
In their book Time Series Analysis, Forecasting, and Control (Prentice Hall, 1994), G. E. P. Box, G. M. Jenkins, and G. C. Reinsel present chemical process concentration readings made every two
Construct and interpret either a digidot plot or a stem and- leaf plot of these data. The 100 annual Wolfer sunspot numbers from 1770 to 1869 follow. (For an interesting analysis and interpretation
In their book Forecasting and Time Series Analysis, 2nd edition (McGraw-Hill, 1990), D. C. Montgomery, L. A. Johnson, and J. S. Gardiner analyze the data in Table 6-5, which are the monthly total
Construct a normal probability plot of the piston ring diameter data in Exercise 6-1. Does it seem reasonable to assume that piston ring diameter is normally distributed?
Construct a normal probability plot of the insulating fluid breakdown time data in Exercise 6-2. Does it seem reasonable to assume that breakdown time is normally distributed?
Construct a normal probability plot of the visual accommodation data in Exercise 6-5. Does it seem reasonable to assume that visual accommodation is normally distributed?
Construct a normal probability plot of the O-ring joint temperature data in Exercise 6-13. Does it seem reasonable to assume that O-ring joint temperature is normally distributed? Discuss any
Construct a normal probability plot of the octane rating data in Exercise 6-14. Does it seem reasonable to assume that octane rating is normally distributed?
Construct a normal probability plot of the cycles to failure data in Exercise 6-15. Does it seem reasonable to assume that cycles to failure is normally distributed?
Construct a normal probability plot of the wine quality rating data in Exercise 6-27. Does it seem reasonable to assume that this variable is normally distributed?

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