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Statistics For Engineers And Scientists 3rd Edition William Navidi - Solutions

The weather in Los Angeles is dry most of the time, but it can be quite rainy in the winter. The rainiest month of the year is February. The following table presents the annual rainfall in Los Angeles, in inches, for each February from 1965 to 2006.a. Construct a stem-and-leaf plot for these
The following table presents the number of students absent in a middle school in northwestern Montana for each school day in January 2008.a. Construct a box plot. b. There was a snowstorm on January 27. Was the number of absences the next day an outlier?
A sample of 100 men has average height 70 in. and standard deviation 2.5 in. A sample of 100 women has average height 64 in. and standard deviation 2.5 in. If both samples are combined, the standard deviation of all 200 heights will be i. Less than 2.5 in. ii. Greater than 2.5 in. iii. Equal to 2.5
Following are summary statistics for two data sets, A and B.a. Compute the inter-quartile ranges for both A and B. b. Do the summary statistics for A provide enough information to construct a box plot? If so, construct the box plot. If not, explain why. c. Do the summary statistics for B provide
Refer to the asphalt data in Example 1.12.a. Construct a box plot for the asphalt data.b. Which values, if any, are outliers?c. Construct a dot plot for the asphalt data.d. For purposes of constructing box plots, an outlier is defined to be a point whose distance from the nearest quartile is more
For the following data:a. Make a scatter plot of y versus x. Is the relationship between x and y approximately linear, or is it nonlinear?b. Compute the natural logarithm of each y value. This is known as making a log transformation of y. make a scatter plot of ln y versus x. Is the relationship
A certain reaction was run several times using each of two catalysts, A and B. The catalysts were supposed to control the yield of an undesirable side product. Results, in units of percentage yield, for 24 runs of catalyst A and 20 runs of catalyst B are as follows:a. Construct a histogram for the
The following histogram presents the distribution of systolic blood pressure for a sample of women. Use it to answer the following questions.a. Is the percentage of women with blood pressures above 130 mm closest to 25%, 50%, or 75%?b. In which interval are there more women: 130-135 or 140-150 mm?
a. Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the frequencies.b. Using the class intervals in the table, construct a histogram in which the heights of the rectangles are equal to the densities.c. Compare the histograms in parts
For each of the following histograms, determine whether the vertical axis has been labeled correctlya.b. c. d.
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, India. One characteristic measured was the speeds of the vehicles
The article "Computing and Using Rural versus Urban Measures in Statistical Applications" (C. Goodall, K. Kafadar, and J. Tukey, The American Statistician, 1998:101-111) discusses methods to measure the degree to which U.S. counties are urban rather than rural. The following frequency table
Water scarcity has traditionally been a major concern in the Canary Islands. Water rights are divided into shares, which are privately owned. The article "The Social Construction of Scarcity the Case of Water in Tenerife (Canary Islands)" (F. Aguilera-Klink, E. Perez-Moriana, and J. Sanchez-Garcia,
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 kg)
Integrated circuits consist of electric channels that are etched onto siliconwafers. Acertain proportion of circuits are defective because of "undercutting," which occurs when too much material is etched away so that the channels, which consist of the unetched portions of the wafers, are too
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
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
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
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
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 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 box contains four bolts. Two of them, labeled #1 and #2, are 5 mm in diameter, and two of them, labeled #3 and #4, are 7 mm in diameter. Bolts are randomly selected until a 5 mm bolt is obtained. The outcomes are the sequences of bolts that can be selected. So one outcome is 1, and another is
In a survey of households with television sets, the proportion of television sets in various types of rooms wasRoom Proportion of TV SetsBedroom...................................0.37Living
Among the cast aluminum parts manufactured on a certain day, 80% were flawless, 15% had only minor flaws, and 5% had major flaws. Find the probability that a randomly chosen part a. Has a flaw (major or minor). b. Has no major flaw.
One drawer in a dresser contains 8 blue socks and 6 white socks. A second drawer contains 4 blue socks and 2 white socks. One sock is chosen from each drawer. What is the probability that they match?
A computer password consists of eight characters. a. How many different passwords is possible if each character may be any lowercase letter or digit? b. How many different passwords are possible if each character may be any lowercase letter or digit, and at least one character must be a digit? c.
In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification
A particular automatic sprinkler system has two different types of activation devices for each sprinkler head. One type has a reliability of 0.9; that is, the probability that it will activate the sprinkler when it should is 0.9. The other type, which operates independently of the first type, has a
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.a. If the wafer
A geneticist is studying two genes. Each gene can be either dominant or recessive. A sample of 100 individuals is categorized as follows.a. What is the probability that a randomly sampled individual, gene 1 is dominant? b. What is the probability that a randomly sampled individual, gene 2 is
A driver encounters two traffic lights on the way to work each morning. Each light is red, yellow, or green. The probabilities of the various combinations of colors are given in the following table:a. What is the probability that the first light is red?b. What is the probability that the second
Nuclear power plants have redundant components in important systems to reduce the chance of catastrophic failure. Assume that a plant has two gauges to measure the level of coolant in the reactor core and that each gauge has probability 0.01 of failing. Assume that one potential cause of gauge
A lot of 10 components contain 3 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. a. Find P(A). b. Find P(B|A). c. Find P(A ∩ B). d. Find P(Ac ∩
Each day, a weather forecaster predicts whether or not it will rain. For 80% of rainy days, she correctly predicts that it will rain. For 90% of non-rainy days, she correctly predicts that it will not rain. Suppose that 10% of days are rainy and 90% are non-rainy. a. What proportion of the
Refer to Exercise 28. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a. Assume that the probability that an item has a flaw is 0.10. If an item is passed by the first inspector, what is the probability that it actually has
A box contains 10 fuses. Eight of them are rated at 10 amperes (A) and the other two are rated at 15 A. Two fuses are selected at random. a. What is the probability that the first fuse is rated at 15 A? b. What is the probability that the second fuse is rated at 15 A, given that the first fuse is
Sickle-cell anemia is an inherited disease in which red blood cells are misshapen and sticky. Sickle cells tend to form clumps in blood vessels, inhibiting the flow of blood. Humans have two genes for sickle-cell anemia, either of which may be S for normal cells or s for sickle cells. A person with
a. If a man tests negative, what is the probability that he actually has the disease? b. For many medical tests, it is standard procedure to repeat the test when a positive signal is given. If repeated tests are independent, what is the probability that a man will test positive on two successive
A system consists of four components, connected as shown in the diagram. Suppose that the components function independently, and that the probabilities of failure are 0.05 for A, 0.03 for B, 0.07 for C, and 0.14 for D. Find the probability that the system functions.
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
On graduation day at a large university, one graduate is selected at random. Let A represent the event that the student is an engineering major, and let B represent the event that the student took a calculus course in college. Which probability is greater, P (A | B) or P (B | A)? Explain.
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
Of people in a certain city who bought a new vehicle in the past year, 12% of them bought a hybrid vehicle, and 5% of them bought a hybrid truck. Given that a person bought a hybrid vehicle, what is the probability that it was a truck?
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
Resistors labeled 100Î© have true resistances that are between 80 Î© and 120 Î©. Let X be the mass of a randomly chosen resistor. The probability density function of X is given bya. What proportion of resistors have resistances less than 90 Î©?b. Find the mean resistance.c. Find the
The lifetime of a transistor in a certain application has a lifetime that is random with probability density functiona. Find the mean lifetime.b. Find the standard deviation of the lifetimes.c. Find the cumulative distribution function of the lifetime.d. Find the probability that the lifetime will
A competing process produces rings whose diameters (in centimeters) vary according to the probability density functionSpecifications call for the diameter to be 10.0±0.1 cm. Which process is better, this one or the one in Exercise 16? Explain.
The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density functiona. What is the probability that the impurity level is greater than 3%?b. What is the probability that the impurity level is between 2% and 3%?c. Find the mean
The concentration of a reactant is a random variable with probability density functiona. What is the probability that the concentration is greater than 0.5?b. Find the mean concentration.c. Find the probability that the concentration is within ±0.1 of the mean.d. Find the standard deviation Ïƒ
The thickness of a washer (in mm) is a random variable with probability density functiona. What is the probability that the thickness is less than 2.5 m?b. What is the probability that the thickness is between 2.5 and 3.5 m?c. Find the mean thickness.d. Find the standard deviation Ïƒ of the
The repair time (in hours) for a certain machine is a random variable with probability density functiona. What is the probability that the repair time is less than 2 hours?b. What is the probability that the repair time is between 1.5 and 3 hours?c. Find the mean repair time.d. Find the cumulative
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:a. Find the mean number of drums ordered.b. Find the variance of the number of drums ordered.c. Find
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 5. Let X represents the number of occupants in a randomly chosen car. a. Find the probability mass function of X. b. Find P(X ≤ 2). c.
A certain type of component is packaged in lots of four. Let X represents the number of properly functioning components in a randomly chosen lot. Assume that the probability that exactly x components function is proportional to x; in other words, assume that the probability mass function of X is
On 100 different days, a traffic engineer counts the number of cars that pass through a certain intersection between 5 P.M. and 5:05 P.M. The results are presented in the following table.a. Let X be the number of cars passing through the intersection between 5 P.M. and 5:05 P.M. on a randomly
If X and Y are independent random variables with means μX = 9.5 and μY = 6.8 and standard deviations σX = 0.4 and σY = 0.1, find the means and standard deviations of the following: a. 3X b. Y − X c. X + 4Y
The number of miles traveled per gallon of gasoline for a certain car has a mean of 25 and a standard deviation of 2. The tank holds 20 gallons.a. Find the mean number of miles traveled per tank.b. Assume the distances traveled are independent for each gallon of gas. Find the standard deviation of
In the article "An Investigation of the Ca-CO3-CaF2- K2SiO3-SiO2-Fe Flux System Using the Submerged Arc Welding Process on HSLA-100 and AISI-1018 Steels" (G. Fredrickson, M.S. thesis, Colorado School of Mines, 1992), the carbon equivalent P of a weld metal is defined to be a linear combination of
Measurements are made on the length and width (in cm) of a rectangular component. Because of measurement error, the measurements are random variables. Let X denote the length measurement and let Y denote the width measurement. Assume that the probability density function of X isAnd that the
The article "Abyssal Peridotites > 3800 Ma from Southern West Greenland: Field Relationships, Petrography, Geochronology, Whole-Rock and Mineral Chemistry of Dunite and Harzburgite Inclusions in the Itsaq Gneiss Complex" (C. Friend, V. Bennett, and A. Nutman, Contrib Mineral Petrol, 2002:71-92)
The lifetime of a certain light bulb in a certain application has mean 700 hours and standard deviation 20 hours. As each bulb burns out, it is replaced with a new bulb. Find the mean and standard deviation of the length of time that five bulbs will last.
A piece of plywood is composed of five layers. The layers are a simple random sample from a population whose thickness has mean 0.125 in. and standard deviation 0.005 in. a. Find the mean thickness of a piece of plywood. b. Find the standard deviation of the thickness of a piece of plywood.
The molarity of a solute in solution is defined to be the number of moles of solute per liter of solution (1 mole = 6.02 × 1023 molecules). If X is the molarity of a solution of magnesium chloride (MgCl2), and Y is the molarity of a solution of ferric chloride (FeCl3), the molarity of chloride ion
The four sides of a picture frame consist of two pieces selected from a population whose mean length is 30 cm with standard deviation 0.1 cm, and two pieces selected from a population whose mean length is 45 cm with standard deviation 0.3 cm. a. Find the mean perimeter. b. Assuming the four pieces
In a certain community, levels of air pollution may exceed federal standards for ozone or for particulate matter on some days. For a particular summer season, let X be the number of days on which the ozone standard is exceeded and let Y be the number of days on which the particulate matter standard
a. Find the conditional probability mass function pY |X (y | 4).b. Find the conditional probability mass function pX|Y (x | 3).c. Find the conditional expectation E(Y | X = 4).d. Find the conditional expectation E(X | Y = 3).In Exercise 9
Let Z represent the total number of vehicles that pass through the toll booth in a one-minute time interval.a. Find Î¼Z.b. Find ÏƒZ.c. Find P (Z = 2).In Exercise 12
a. Find the conditional probability mass function pY |X (y | 3).b. Find the conditional probability mass function pX|Y (x | 1).c. Find the conditional expectation E(Y | X = 3).d. Find the conditional expectation E(X | Y = 1).In Exercise 12
Refer to Exercise 18.a. Find Cov(X, Y).b. Find ÏX,Y.c. Find the conditional probability density function fY |X (y | 0.5).d. Find the conditional expectation E(Y | X = 0.5).In Exercise 18
The lifetime of a certain component, in years, has probability density functionTwo such components, whose lifetimes are independent, are available. As soon as the first component fails, it is replaced with the second component. Let X denotes the lifetime of the first component, and let Y denote the
An investor has $100 to invest, and two investments between which to divide it. If she invests the entire amount in the first investment, her return will be X, while if she invests the entire amount in the second investment, her return will be Y. Both X and Y have mean $6 and standard deviation
Let R denote the resistance of a resistor that is selected at random from a population of resistors that are labeled 100Ω. The true population means resistance is μR = 100 Ω, and the population standard deviation is σR = 2 Ω. The resistance is measured twice with an ohmmeter. Let M1 and M2
Let X and Y be random variables, and a and b be constants.a. Prove that Cov(aX, bY ) = ab Cov(X,Y ).b. Prove that if a > 0 and b > 0, then ρaX,bY = ρX,Y. Conclude that the correlation coefficient is unaffected by changes in units.
Let X and Y be jointly distributed random variables. This exercise leads you through a proof of the fact that −1 ≤ ρX,Y ≤ 1. a. Express the quantity V(X − (σX/σY) Y) in terms of σX, σY, and Cov(X, Y ). b. Use the fact that V(X − (σX/σY)Y) ≥ 0 and Cov(X, Y) = ρX,YσXσY to show
a. Find the conditional probability mass function pY |X (y |0). b. Find the conditional probability mass function pX|Y (x |1). c. Find the conditional expectation E(Y | X = 0). d. Find the conditional expectation E(X | Y = 1).
Refer to Exercise 30. An equation to predict the ductility of a titanium weld is Y = 7.84C +11.44N + O − 1.58Fe, where Y is the oxygen equivalence used to predict ductility, and C, N, O, and Fe are the amounts of carbon, nitrogen, oxygen, and iron, respectively, in weight percent, in the weld.
Let a, b, c, d be any numbers with aIn other words, f (x, y) is constant on the rectangle a a. Show that k = 1/((b - a)(d - c)).b. Show that the marginal density of X is fX (x) = 1/(b - a) for a c. Show that the marginal density of Y is fY (y) = 1/(d - c) for c d. Use parts (a), (b),
The total number of assemblies that fail to meet specifications is X + Y. a. Find μX+Y. b. Find σX+Y . c. Find P(X + Y = 3).
Assume that the cost of repairing an assembly whose clearance is too little is $2, and the cost of repairing an assembly whose clearance is too much is $3. a. Express the total cost of repairs in terms of X and Y. b. Find the mean of the total cost of repairs. c. Find the standard deviation of the
Bolts manufactured for a certain purpose may be classified as acceptable (suitable for the intended purpose), downgraded (unsuitable for the intended purpose but acceptable for a different purpose), or scrap (unsuitable for any purpose). In a lot of 500 bolts, let X be the number that are
A system consists of four components connected as shown.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?
There are two fuses in an electrical device. Let X denotes the lifetime of the first fuse, and let Y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y isa. Find P(X < 2 and Y < 3).b. Find the probability that both fuses last at
A snowboard manufacturer has three plants, one in the eastern United States, one in the western United States, and one in Canada. Production records show that the U.S. plants each produced 10,000 snowboards last month, while the Canadian plant produced 8000 boards. Of all the boards manufactured in
Six new graduates are hired by an engineering firm. Each is assigned at random to one of six cubicles arranged in a row in the back of the room that houses the engineering staff. Two of the graduates are Bill and Cathy. What is the probability that they are assigned adjacent cubicles?
Let X and Y be independent random variables with μX = 2, σX = 1, μY = 2, and σY = 3. Find the means and variances of the following quantities. a. 3X b. X + Y c. X − Y d. 2X + 6Y
A steel manufacturer is testing a new additive for manufacturing an alloy of steel. The joint probability mass function of tensile strength (in thousands of pounds/in2) and additive concentration isa. What are the marginal probability mass functions for X (additive concentration) and Y (tensile
Refer to Exercise 19.a. Compute the conditional mass function p Y|X (y | 0.06).b. Compute the conditional mass function p X|Y (x | 100).c. Compute the conditional expectation E(Y | X = 0.06).d. Compute the conditional expectation E(X | Y = 100).In Exercise 19
The article "Uncertainty and Climate Change" (G. Heal and B. Kristrom, Environmental and Resource Economics, 2002:3-39) considers three scenarios, labeled A, B, and C, for the impact of global warming on income. For each scenario, a probability mass function for the loss of income is specified.
A box contains four 75Wlightbulbs, three 60Wlightbulbs, and three burned-out light bulbs. Two bulbs are selected at random from the box. Let X represent the number of 75 W bulbs selected, and let Y represent the number of 60 W bulbs selected. a. Find the joint probability mass function of X and
Refer to Exercise 26.a. Find μX.b. Find σ2X.c. Find Cov (X,Y).d. Find σX,σY.In Exercise 26
A penny and a nickel are tossed. The penny has probability 0.4 of coming up heads, and the nickel has probability 0.6 of coming up heads. Let X = 1 if the penny comes up heads, and let X = 0 if the penny comes up tails. Let Y = 1 if the nickel comes up heads, and let Y = 0 if the nickel comes up
Silicon wafers are used in the manufacture of integrated circuits. Of the wafers manufactured by a certain process, 10% have resistances below specification and 5% have resistances above specification. a. What is the probability that the resistance of a randomly chosen wafer does not meet the
A box contains three cards, labeled 1, 2, and 3. Two cards are chosen at random, with the first card being replaced before the second card is drawn. Let X represents the number on the first card, and let Y represent the number on the second card. a. Find the joint probability mass function of X and
This exercise will lead you through a proof of Chebyshev’s inequality. Let X be a continuous random variable with probability density function f (x). Suppose that P(X < 0) = 0, so f (x) = 0 for x ≤ 0.a. Show thatb. Let k >0 be a constant. Show that μX ≥c. Use part (b) to show that P(X
Blood is taken from each of n individuals to be tested for a certain disease. Rather than test each sample separately, a pooled method is used in an attempt to reduce the number of tests needed. Part of each blood sample is taken, and these parts are combined to form a pooled sample. The pooled
Four bricks are sampled from a large load and the crushing strength of each is measured to determine whether it meets a specification. If any of the four fail to meet the specification the load will be returned. If in fact 10% of the bricks in the load fail to meet the specification, what is the
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
Two dice are rolled. Given that two different numbers come up, what is the probability that one of the dice comes up 6?
The length of a rod was measured eight times. The measurements in centimeters, in the order they were taken, were 21.20, 21.22, 21.25, 21.26, 21.28, 21.30, 21.32, 21.35. a. Do these measurements appear to be a random sample from a population of possible measurements? Why or why not? b. Is it
A person stands on a bathroom scale. The reading is 150 lb. After the person gets off the scale, the reading is 2 lb. a. Is it possible to estimate the uncertainty in this measurement? If so, estimate it. If not, explain why not. b. Is it possible to estimate the bias in this measurement? If so,

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