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Principles Of Statistics For Engineers And Scientists 2nd International Edition William Navidi - Solutions

Elongations (in %) of steel plates treated with aluminum are random with probability density function f(x) ={ x 250 20 < x < 30 0 otherwisea. What proportion of steel plates have elongations greater than 25%?b. Find the mean elongation.c. Find the variance of the elongations.d. Find the standard
Resistors labeled 100 Ω have true resistances that are between 80 Ω and 120 Ω. Let X be the mass of a randomly chosen resistor. The probability density function of X is given by f(x) =⎧⎪⎨⎪⎩x − 80 800 80 < x < 120 0 otherwisea. What proportion of resistors have resistances less than
After manufacture, computer disks are tested for errors. Let X be the number of errors detected on a randomly chosen disk. The following table presents values of the cumulative distribution function F(x) of X.x F(x)0 0.41 1 0.72 2 0.83 3 0.95 4 1.00a. What is the probability that two or fewer
A computer sends a packet of information along a channel and waits for a return signal acknowledging that the packet has been received. If no acknowledgment is received within a certain time, the packet is resent. Let X represent the number of times the packet is sent. Assume that the probability
The element titanium has five stable occurring isotopes, differing from each other in the number of neutrons an atom contains. If X is the number of neutrons in a randomly chosen titanium atom, the probability mass function of X is given as follows:x 24 25 26 27 28 p(x) 0.0825 0.0744 0.7372 0.0541
Let X represent the number of occupants in a randomly chosen car.a. Find the probability mass function of X.b. Find P(X ≤ 2).c. Find P(X > 3).d. Find ????X.e. Find ????X.
A survey of cars on a certain stretch of highway during morning commute hours showed that 70% had only one occupant, 15% had 2, 10% had 3, 3% had 4, and 2% had
Let X represent the number of tires with low air pressure on a randomly chosen car.a. Which of the three functions below is a possible probability mass function of X? Explain.x 01234 p1(x) 0.2 0.2 0.3 0.1 0.1 p2(x) 0.1 0.3 0.3 0.2 0.2 p3(x) 0.1 0.2 0.4 0.2 0.1b. For the possible probability mass
A chemical supply company ships a certain solvent in 10-gallon drums. Let X represent the number of drums ordered by a randomly chosen customer. Assume X has the following probability mass function:x 12345 p(x) 0.4 0.2 0.2 0.1 0.1a. Find the mean number of drums ordered.b. Find the variance of the
Computer chips often contain surface imperfections.For a certain type of computer chip, the probability mass function of the number of defects X is presented in the following table.x 01 2 3 4 p(x) 0.4 0.3 0.15 0.10 0.05a. Find P(X ≤ 2).b. Find P(X > 1).c. Find ????X.d. Find ????2 X.
Determine whether each of the following random variables is discrete or continuous.a. The number of heads in 100 tosses of a coin.b. The length of a rod randomly chosen from a day’s production.c. The final exam score of a randomly chosen student from last semester’s engineering statistics
An electronic message consists of a string of bits (0s and 1s). The message must pass through two relays before being received. At each relay the probability is 0.1 that the bit will be reversed before being relayed (i.e., a 1 will be changed to a 0, or a 0 to a 1). Find the probability that the
If A and B are independent events, prove that the following pairs of events are independent: Ac and B, A and Bc, and Ac and Bc.
A system contains two components, C and D, connected in parallel as shown in the diagram.Assume C and D function independently. For the system to function, either C or D must function.a. If the probability that C fails is 0.08 and the probability that D fails is 0.12, find the probability that the
A system contains two components, A and B, connected in series, as shown in the diagram.Assume A and B function independently. For the system to function, both components must function.a. If the probability that A fails is 0.05, and the probability that B fails is 0.03, find the probability that
A system consists of four components connected as shown in the following diagram:Assume A, B, C, and D function independently.If the probabilities that A, B, C, and D fail are 0.1, 0.2, 0.05, and 0.3, respectively, what is the probability that the system functions? A B C
A system consists of four components connected as shown in the following diagram:Assume A, B, C, and D function independently.If the probabilities that A, B, C, and D fail are 0.10, 0.05, 0.10, and 0.20, respectively, what is the probability that the system functions? A B D
The following table presents the 100 senators of the 116th U.S. Congress on January 3, 2019, classified by political party affiliation and gender.Male Female Democrat 28 17 Republican 45 8 Independent 2 0 Source: The Law Library of Congress.A senator is selected at random from this group. Compute
A car dealer sold 750 automobiles last year. The following table categorizes the cars sold by size and color and presents the number of cars in each category. A car is to be chosen at random from the 750 for which the owner will win a lifetime of free oil changes.Color Size White Black Red Grey
A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows.Gene 2 Gene 1 Dominant Recessive Dominant 56 24 Recessive 14 6a. What is the probability that in a randomly sampled individual, Gene 1 is dominant?b. What is the
Refer to Exercise 7. Let E1 be the event that the wafer comes from Lot A, and let E2 be the event that the wafer is conforming. Are E1 and E2 independent?Explain.
A population of 600 semiconductor wafers contains wafers from three lots. The wafers are categorized by lot and by whether they conform to a thickness specification. The following table presents the number of wafers in each category. A wafer is chosen at random from the population.Lot Conforming
Refer to Exercise 5. Resistors are randomly selected from the box, one by one, until a 100 Ω resistor is selected.a. What is the probability that the first two resistors are both 50 Ω?b. What is the probability that a total of two resistors are selected from the box?c. What is the probability
A box contains 15 resistors. Ten of them are labeled 50 Ω and the other five are labeled 100 Ω. Two resistors are selected at random.a. What is the probability that the first resistor is 100 Ω?b. What is the probability that the second resistor is 100 Ω, given that the first resistor is 50
Let A and B be events with P(A) = 0.8 and P(A∩B) =0.2. For what value of P(B) will A and B be independent?
Suppose that 90% of bolts and 85% of nails meet specifications. One bolt and one nail are chosen independently.a. What is the probability that both meet specifications?b. What is the probability that neither meets specifications?c. What is the probability that at least one of them meets
A drag racer has two parachutes, a main and a backup, that are designed to bring the vehicle to a stop after the end of a run. Suppose that the main chute deploys with probability 0.99, and that if the main fails to deploy, the backup deploys with probability 0.98.a. What is the probability that
Suppose that start-up companies in the area of biotechnology have probability 0.2 of becoming profitable and that those in the area of information technology have probability 0.15 of becoming profitable.A venture capitalist invests in one firm of each type.Assume the companies function
Let V be the event that a computer contains a virus, and let W be the event that a computer contains a worm. Suppose P(V) = 0.15, P(W) = 0.05, and P(V ∪ W) = 0.17.a. Find the probability that the computer contains both a virus and a worm.b. Find the probability that the computer contains neither
Let S be the event that a randomly selected college student has taken a statistics course, and let C be the event that the same student has taken a chemistry course. Suppose P(S) = 0.4, P(C) = 0.3, and P(S ∩ C) = 0.2.a. Find the probability that a student has taken statistics, chemistry, or
Six hundred paving stones were examined for cracks, and 15 were found to be cracked. The same 600 stones were then examined for discoloration, and 27 were found to be discolored. A total of 562 stones were neither cracked nor discolored. One of the 600 stones is selected at random.a. Find the
All the fourth-graders in a certain elementary school took a standardized test. A total of 85% of the students were found to be proficient in reading, 78% were found to be proficient in mathematics, and 65% were found to be proficient in both reading and mathematics. A student is chosen at
Each bolt is checked to determine whether it is torqued correctly. Let A be the event that all the bolts are torqued correctly, let B be the event that the #3 bolt is not torqued correctly, let C be the event that exactly one bolt is not torqued correctly, and let D be the event that bolts #5 and
A flywheel is attached to a crankshaft by 12 bolts, numbered 1 through
True or false: If A and B are mutually exclusive,a. P(A ∪ B) = 0b. P(A ∩ B) = 0c. P(A ∪ B) = P(A ∩ B)d. P(A ∪ B) = P(A) + P(B)
Human blood may contain either or both of two antigens, A and B. Blood that contains only the A antigen is called type A, blood that contains only the B antigen is called type B, blood that contains both antigens is called type AB, and blood that contains neither antigen is called type O. At a
A system contains two components, A and B. The system will function only if both components function.The probability that A functions is 0.98, the probability that B functions is 0.95, and the probability that either A or B functions is 0.99. What is the probability that the system functions?
A system contains two components, A and B. The system will function so long as either A or B functions.The probability that A functions is 0.95, the probability that B functions is 0.90, and the probability that both function is 0.88. What is the probability that the system functions?
According to a report by the Agency for Healthcare Research and Quality, the age distribution for people admitted to a hospital for an asthma-related illness was as follows.Age (years) Proportion Less than 1 0.02 1–17 0.25 18–44 0.19 45–64 0.30 65–84 0.20 85 and up 0.04a. What is the
A company audit showed that of all bills that were sent out, 71% of them were paid on time, 18% were paid up to 30 days late, 9% were paid between 31 and 90 days late, and 2% remained unpaid after 90 days.One bill is selected at random.a. What is the probability that the bill was paid on time?b.
A section of an exam contains four True–False questions. A completed exam paper is selected at random, and the four answers are recorded.a. List all 16 outcomes in the sample space.b. Assuming the outcomes to be equally likely, find the probability that all the answers are the same.c. Assuming
A die (six faces) has the number 1 painted on three of its faces, the number 2 painted on two of its faces, and the number 3 painted on one face. Assume that each face is equally likely to come up.a. Find a sample space for this experiment.b. Find P(odd number).c. If the die were loaded so that the
The probability that a bolt meets a strength specification is 0.87. What is the probability that the bolt does not meet the specification?
Let y be the height in meters from which a bomb is dropped, let x be the time in seconds for the bomb to strike the ground, let u = x2, and let v = √y. The relationship between x and y is given by y = 4.9x2. For each of the following pairs of variables, state whether the correlation coefficient
In a test of military ordnance, a large number of bombs were dropped on a target from various heights.The initial velocity of the bombs in the direction of the ground was
The article “Estimating Population Abundance in Plant Species With Dormant Life-Stages: Fire and the Endangered Plant Grevillea caleye R. Br.” (T. Auld and J. Scott, Ecological Management and Restoration, 2004:125–129) presents estimates of population sizes of a certain rare shrub in areas
The article “Experimental Measurement of Radiative Heat Transfer in Gas–Solid Suspension Flow System” (G. Han, K. Tuzla, and J. Chen, AIChe Journal, 2002:1910–1916) discusses the calibration of a radiometer. Several measurements were made on the electromotive force readings of the
A scatterplot contains three points: (−1,−1),(0,0), (1,1). A fourth point, (2,y), is to be added to the plot. Let r represent the correlation between x and y.a. Find the value of y so that r = 1.b. Find the value of y so that r = 0.c. Explain why there is no value of y for which r = −1.
A mixture of sucrose and water was heated on a hot plate, and the temperature (in ◦C) was recorded each minute for 20 minutes by three thermocouples. The results are shown in the following table.a. Compute the least-squares line for estimating the temperature as a function of time, using T1 as
In a sample of adults, would the correlation between age and the year graduated from high school be closest to −1, −0.5, 0, 0.5, or 1? Explain.
In an accelerated life test, units are operated under extreme conditions until failure. In one such test, 12 motors were operated under high temperature conditions. The ambient temperatures (in ◦C) and lifetimes(in hours) are presented in the following table:a. Construct a scatterplot of lifetime
A simple random sample of 100 men aged 25–34 averaged 70 inches in height and had a standard deviation of 3 inches. Their incomes averaged $34,900 and had a standard deviation of $17,200. Fill in the blank: From the least-squares line, we would predict that the income of a man 70 inches tall
Carrie and Ryan have both computed the slope of the least-squares line using data for which the standard deviations of the x-values and the y-values are equal.Carrie gets a value of 0.5 for the slope, and Ryan gets a value of 2. One of them is right. Which one?
An engineer wants to predict the value for y when x = 4.5, using the following data set.xyz = ???????? y x yz = ???????? y 1 0.2 −1.61 6 2.3 0.83 2 0.3 −1.20 7 2.9 1.06 3 0.5 −0.69 8 4.5 1.50 4 0.5 −0.69 9 8.7 2.16 5 1.3 0.26 10 12.0 2.48a. Construct a scatterplot of the points (x, y).b.
The correlation between curing time and firmness was computed to be r =0.5. Find the equation of the least-squares line to predict firmness from pectin concentration.
Varying amounts of pectin were added to canned jellies, to study the relationship between pectin concentration in percent (x) and a firmness index (y).The means and standard deviations of the x and y values were x = 3, sx = 0.5, y = 50, sy =
Curing times in days (x) and compressive strengths in MPa (y) were recorded for several concrete specimens. The means and standard deviations of the x and y values were x = 5, sx = 2, y = 1350, sy = 100.The correlation between curing time and compressive strength was computed to be r = 0.7. Find
Moisture content in percent by volume (x) and conductivity in mS/m (y) were measured for 50 soil specimens. The means and standard deviations were x = 8.1, sx = 1.2, y = 30.4, sy = 1.9. The correlation between conductivity and moisture was computed to be r = 0.85. Find the equation of the
A least-squares line is fit to a set of points. If the total sum of squares is ∑(yi − y)2 = 181.2, and the error sum of squares is ∑(yi − ŷi)2 = 33.9, compute the coefficient of determination r2.
A least-squares line is fit to a set of points. If the total sum of squares is ∑(yi − y)2 = 9615, and the error sum of squares is ∑(yi − ŷi)2 = 1450, compute the coefficient of determination r2.
For a certain scatterplot, the value of the correlation coefficient is r = 0.5. Which of the following statements is correct?i. The total sum of squares is half as much as the regression sum of squares.ii. The regression sum of squares is half as much as the total sum of squares.iii. The total sum
In an experiment to determine corrosion rates, steel plates were placed in a solution of 10% hydrochloric acid (HCl) for various periods of time (in hours), and the weight loss (in mg) was measured. Following are the results.Time 2 4 6 8 10 12 Weight loss 0.7 6.9 7.2 11.9 16.2 22.5a. Compute the
Following are measurements of strain (in %) and stress (in MPa) for a sample of copper bars.Stress Strain Stress Strain 8.2 77.6 13.4 80.9 9.6 78.8 13.5 81.3 11.0 78.9 14.7 82.2 12.0 80.2 14.9 82.7a. Compute the least-squares line using strain as the dependent variable (y) and stress as the
Ultimate strengths (in MPa) were measured at several temperatures (in ◦C) for three types of plastic. The results follow.a. Construct a scatterplot for each of the three data sets.b. For each data set, say whether the least-squares line is appropriate for summarizing the data, and explain why.
The following table presents measurements of hardness (in durometers) for tire treads containing various percentages of reclaimed rubber.a. Construct a scatterplot of hardness (y) versus percent reclaimed rubber (x).b. Compute the least-squares line for predicting hardness from percent reclaimed
A sample of 10 households was monitored for one year. The household income (in $1000s) and the amount of energy consumed (in 1010 joules) were determined. The results follow.Income Energy Income Energy 31 16.0 96 98.3 40 40.2 70 93.8 28 29.8 100 77.1 48 45.6 145 114.8 195 184.6 78 67.0a. Construct
For a sample of 12 trees, the volume of lumber (in m3)and the diameter (in cm) at a fixed height above ground level was measured. The results were as follows.Diameter Volume Diameter Volume 35.1 0.81 33.8 0.80 48.4 1.39 45.3 1.69 47.9 1.31 25.2 0.30 35.3 0.67 28.5 0.19 47.3 1.46 30.1 0.63 26.4 0.47
Concrete expands both horizontally and vertically over time. The article “Evaluation of the Expansion Attained to Date by Concrete Affected by AlkaliSilica Reaction. Part III: Application to Existing Structures” (M. Berub ´e, N. Smaoui, et al., ´ Canadian Journal of Civil Engineering,
The article “Effect of Environmental Factors on Steel Plate Corrosion Under Marine Immersion Conditions” (C. Soares, Y. Garbatov, and A. Zayed, Corrosion Engineering, Science and Technology, 2011:524–541) describes an experiment in which nine steel specimens were submerged in seawater at
Structural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article “Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network” (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863–872)
A blood pressure measurement consists of two numbers: the systolic pressure, which is the maximum pressure taken when the heart is contracting, and the diastolic pressure, which is the minimum pressure taken at the beginning of the heartbeat. Blood pressures were measured, in mmHg, for a sample of
Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. The article “An Intelligent Insole for Diabetic Patients with the Loss of Protective Sensation” (Kimberly Anderson, M.S. Thesis, Colorado School of Mines)
In a study relating the degree of warping, in mm, of a copper plate (y) to temperature in ◦C (x), the following summary statistics were calculated: n = 40,∑n i=1(xi − x)2 = 98,775, ∑n i=1(yi − y)2 = 19.10, x = 26.36, y = 0.5188, ∑n i=1(xi − x)(yi − y) = 826.94.a. Compute the
One of the earliest uses of the correlation coefficient was by Sir Francis Galton, who computed the correlation between height and forearm length for a sample of adult men. Assume that the least-squares line for predicting forearm length (y) from height (x) is y = −0.2967 + 0.2738x. Both forearm
In a study of the relationship between the Brinell hardness (x) and tensile strength in ksi (y) of specimens of cold drawn copper, the least-squares line was y = −196.32 + 2.42x.a. Predict the tensile strength of a specimen whose Brinell hardness is 102.7.b. If two specimens differ in their
Each month for several months, the average temperature in ◦C (x) and the amount of steam in kg (y) consumed by a certain chemical plant were measured.The least-squares line computed from the resulting data is y = 245.82 + 1.13x.a. Predict the amount of steam consumed in a month where the average
Another chemical engineer is studying the same process as in Exercise 7 and uses the following experimental matrix.a. Compute the correlation between temperature and yield, between stirring rate and yield, and between temperature and stirring rate.b. Do these data provide good evidence that the
A chemical engineer is studying the effect of temperature and stirring rate on the yield of a certain product.The process is run 16 times, at the settings indicated in the following table. The units for yield are percent of a theoretical maximum.a. Compute the correlation between temperature and
In a study of ground motion caused by earthquakes, the peak velocity (in m/s) and peak acceleration(in m/s2) were recorded for five earthquakes. The results are presented in the following table.Velocity 1.54 1.60 0.95 1.30 2.92 Acceleration 7.64 8.04 8.04 6.37 3.25a. Compute the correlation
An investigator collected data on heights and weights of college students. The correlation between height and weight for men was about 0.6, and for women it was about the same. If men and women are taken together, will the correlation between height and weight be more than 0.6, less than 0.6, or
True or false, and explain briefly:a. If the correlation coefficient is positive, then above-average values of one variable are associated with above-average values of the other.b. If the correlation coefficient is negative, then below-average values of one variable are associated with
For each of the following scatterplots, state whether the correlation coefficient is an appropriate summary, and explain briefly.
For each of the following data sets, explain why the correlation coefficient is the same as for the data set in Exercise 1.a. x 12345 y 4 2 8 6 14b. x 13 23 33 43 53 y 4 2 8 6 14 c.x 32548 y 2 4 6 8 10
Compute the correlation coefficient for the following data set.x 12345 y 21437
The article “Hydrogeochemical Characteristics of Groundwater in a Mid-Western Coastal Aquifer System” (S. Jeen, J. Kim, et al., Geosciences Journal, 2001:339–348) presents measurements of various properties of shallow groundwater in a certain aquifer system in Korea. Following are
The article “ The Ball-on-Three-Ball Test for Tensile Strength: Refined Methodology and Results for Three Hohokam Ceramic Types” (M. Beck, American Antiquity, 2002:558–569) discusses the strength of ancient ceramics. Several specimens of each of three types of ceramic were tested. The loads
In the article “Occurrence and Distribution of Ammonium in Iowa Groundwater” (K. Schilling, Water Environment Research, 2002:177–186), ammonium concentrations (in mg/L) were measured at a total of 349 alluvial wells in the state of Iowa. The mean concentration was 0.27, the median was 0.10,
The article “Vehicle-Arrival Characteristics at Urban Uncontrolled Intersections” (V. Rengaraju and V. Rao, Journal of Transportation Engineering, 1995:317–323) presents data on traffic characteristics at 10 intersections in Madras (now Chennai), India. One characteristic measured was the
True or false: In any boxplot,a. The length of the whiskers is equal to 1.5 IQR, where IQR is the interquartile range.b. The length of the whiskers may be greater than 1.5 IQR, where IQR is the interquartile range.c. The length of the whiskers may be less than 1.5 IQR, where IQR is the
Concerning the data represented in the following boxplot, which one of the following statements is true?i. The mean is greater than the median.ii. The mean is less than the median.iii. The mean is approximately equal to the median.
The article “The Selection of Yeast Strains for the Production of Premium Quality South African Brandy Base Products” (C. Steger and M. Lambrechts, Journal of Industrial Microbiology and Biotechnology, 2000:431– 440) presents detailed information on the volatile compound composition of base
There are 15 numbers on a list, and the mean is 25.The smallest number on the list is changed from 12.9 to 1.29.a. Is it possible to determine by how much the mean changes? If so, by how much does it change?b. Is it possible to determine the value of the mean after the change? If so, what is the
There are 15 numbers on a list, and the smallest number is changed from 12.9 to 1.29.a. Is it possible to determine by how much the mean changes? If so, by how much does it change?b. Is it possible to determine the value of the mean after the change? If so, what is the value?c. Is it possible to
The smallest number on a list is changed from 12.9 to 1.29.a. Is it possible to determine by how much the mean changes? If so, by how much does it change?b. Is it possible to determine by how much the median changes? If so, by how much does it change?What if the list consists of only two numbers?c.
A coin is tossed twice and comes up heads both times.Someone says, “There’s something wrong with this coin. A coin is supposed to come up heads only half the time, not every time.”a. Is it reasonable to conclude that something is wrong with the coin? Explain.b. If the coin came up heads 100
The specification for the pull strength of a wire that connects an integrated circuit to its frame is 10 g or more. Units made with aluminum wire have a defect rate of 10%. A redesigned manufacturing process, involving the use of gold wire, is being investigated.The goal is to reduce the rate of
Suppose that every worker in a company received a$2000-per-year raise. How does this affect the mean salary? The standard deviation of the salaries?
In a certain company, every worker received a 5%raise. How does this affect the mean salary? The standard deviation of the salaries?
Refer to the asphalt data in Example 1.8 (page 16).a. Construct a boxplot for the asphalt data.b. Which values, if any, are outliers?c. Construct a dotplot for the asphalt data.d. For purposes of constructing boxplots, an outlier is defined to be a point whose distance from the nearest quartile is
Following are summary statistics for two data sets, A and B.A B Minimum 0.066 −2.235 1st Quartile 1.42 5.27 Median 2.60 8.03 3rd Quartile 6.02 9.13 Maximum 10.08 10.51a. Compute the interquartile ranges for both A and B.b. Do the summary statistics for A provide enough information to construct a

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