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Statistics For Engineers And Scientists 4th Edition William Navidi - Solutions

The article €œAnalysis of Time Head ways on Urban Roads: Case Study from Riyadh€ (A. Al-Ghamdi, Journal of Transportation Engineering, 2001: 289€“294) presents a model for the time elapsed between the arrival of consecutive vehicles on urban roads. Following are 137 arrival times (in
A new centrifugal pump is being considered for an application involving the pumping of ammonia. The specification is that the flow rate be more than 5 gallons per minute (gpm). In an initial study, eight runs were made. The average flow rate was 6.5 gpm and the standard deviation was 1.9 gpm. If
The article “Supply Voltage Quality in Low-Voltage Industrial Networks of Estonia” (T. Vinnal, K. Janson, et al., Estonian Journal of Engineering, 2012:102–126) presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these networks is 232
The article “A Music Key Detection Method Based on Pitch Class Distribution Theory” (J. Sun, H. Li, and L. Ma, International Journal of Knowledge-based and Intelligent Engineering Systems, 2011:165–175) describes a method of analyzing digital music files to determine the key in which the
The article €œReaction Modeling and Optimization Using Neural Networks and Genetic Algorithms: Case Study Involving TS-1-Catalyzed Hydroxylation of Benzene€ (S. Nandi, P. Mukherjee, et al., Industrial and Engineering Chemistry Research, 2002:2159€“2169) presents
The article “Influence of Penetration Rate on Penetrometer Resistance” (J. Oliveira, M. Almeida, et al., Journal of Geotechnical and Geoenvironmental Engineering, 2011:695–703) presents measures of penetration resistance, expressed as a multiple of a standard quantity, for a certain
Scores on an IQ test are normally distributed. A sample of 25 IQ scores had variance s2 = 64. The developer of the test claims that the population variance is σ2 = 225. Do these data provide sufficient evidence to contradict this claim?
The article “Measurement of Complex Permittivity of Asphalt Paving Materials” (J. Shang, J. Umana, et al., Journal of Transportation Engineering, 1999:347–356) compared the dielectric constants between two types of asphalt, HL3 and HL8, commonly used in pavements. For 42 specimens of HL3
If P = 0.01, which is the best conclusion?i. H0 is definitely false.ii. H0 is definitely true.iii. There is a 1% probability that H0 is true.iv. H0 might be true, but it’s unlikely.v. H0 might be false, but it’s unlikely.vi. H0 is plausible.
The article “HIV-positive Smokers Considering Quitting: Differences by Race/Ethnicity” (E. Lloyd- Richardson, C. Stanton, et al., Am J Health Behav, 2008:3–15) surveyed 444 HIV-positive smokers. Of these, 281 were male and 163 were female. Consider this to be a simple random sample. Can you
The article €œEstimation of Mean Arterial Pressure from the Oscillometric Cuff Pressure: Comparison of Different Techniques€ (D. Zheng, J. Amoore, et al., Med Biol Eng Comput, 2011:33€“39) describes a study comparing two methods of measuring mean arterial blood
Refer to Exercise 6 in Section 5.10. Let Î¼ represent the population mean compressive strength, in MPa. Generate 1000 bootstrap samples.a. Using the bootstrap data you generated, which of these null hypotheses can be rejected at the 5% level, using method 1 on page 390?b. Using the bootstrap data
A geologist is making repeated measurements (in grams) on the mass of a rock. It is not known whether the measurements are a random sample from an approximately normal population. Below are three sets of replicate measurements, listed in the order they were made. For each set of readings, state
A simple random sample consists of 65 lengths of piano wire that were tested for the amount of extension under a load of 30 N. The average extension for the 65 lines was 1.102 mm and the standard deviation was 0.020 mm. Let μ represent the mean extension for all specimens of this type of piano
Resistors labeled as 100 Ω are purchased from two different vendors. The specification for this type of resistor is that its actual resistance be within 5% of its labeled resistance. In a sample of 180 resistors from vendor A, 150 of them met the specification. In a sample of 270 resistors
The thicknesses of eight pads designed for use in aircraft engine mounts are measured. The results, in mm, are 41.83, 41.01, 42.68, 41.37, 41.83, 40.50, 41.70, and 41.42. Assume that the thicknesses are a sample from an approximately symmetric distribution.a. Can you conclude that the mean
Refer to Exercise 1. The P-value for fertilizer C was 0.03. Use the Bonferroni correction to produce a reliable P-value for this fertilizer. Can you reject H0?Refer to Exercise 1An agricultural scientist tests six types of fertilizer, labeled A, B, C, D, E, and F, to determine whether any of them
A process for a certain type of ore is designed to reduce the concentration of impurities to less than 2%. It is known that the standard deviation of impurities for processed ore is 0.6%. Let μ represent the mean impurity level, in percent, for ore specimens treated by this process. The impurity
In a study of the relationship of the shape of a tablet to its dissolution time, 6 disk-shaped ibuprofen tablets and 8 oval-shaped ibuprofen tablets were dissolved in water. The dissolve times, in seconds, were as follows:Can you conclude that the mean dissolve times differ between the two shapes?
A random sample of size 29 from a normal distribution has variance s2 = 24. Test H0 : σ2 ≥ 30 versus H1 : σ2 < 30.
A group of 15 swimmers is chosen to participate in an experiment to see if a new breathing style will improve their stamina. Each swimmer’s pulse recovery rate is measured after a 20 minute workout using the old breathing style. The swimmers practice the new style for two weeks, and then measure
At an assembly plant for light trucks, routine monitoring of the quality of welds yields the following data:Can you conclude that the quality varies among shifts?a. State the appropriate null hypothesis.b. Compute the expected values under the null hypothesis.c. Compute the value of the chi-square
Integrated circuits consist of electric channels that are etched onto silicon wafers. A certain 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
Refer to Exercise 6 in Section 5.10. Let µ represent the population mean compressive strength, in MPa. Consider the following null hypotheses:a. Using the bootstrap data presented in Exercise 6 in Section 5.10, which of these null hypotheses can be rejected at the 5% level if a confidence interval
The article €œImproved Bioequivalence Assessment of Topical Dermatological Drug Products Using Dermatopharmacokinetics€ (B. N€™Dri-Stempfer, W. Navidi, R. Guy, and A. Bunge, Pharmaceutical Research, 2009:316€“328) described a study comparing the amounts of
An agricultural scientist tests six types of fertilizer, labeled A, B, C, D, E, and F, to determine whether any of them produces an increase in the yield of lima beans over that obtained with the current fertilizer. For fertilizer C, the increase in yield is statistically significant at the 0.05
True or false:a. If we reject H0, then we conclude that H0 is false.b. If we do not reject H0, then we conclude that H0 is true.c. If we reject H0, then we conclude that H1 is true.d. If we do not reject H0, then we conclude that H1 is false.
A random sample of size 11 from a normal distribution has variance s2 = 96. Test H0 : σ2 ≤ 50 versus H1 : σ2 > 50.
For which P-value is the null hypothesis more plausible: P = 0.5 or P = 0.05?
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.a. Find P(X ‰¤ 2).b. Find P(X > 1).c. Find Î¼X.d. Find Ïƒ2X. 3 0.4 0.3 0.15
A process that manufactures piston rings produces rings whose diameters (in centimeters) vary according to the probability density function.a. Find the mean diameter of rings manufactured by this process.b. Find the standard deviation of the diameters of rings manufactured by this process. Equation
The number of bytes downloaded per second on an information channel has mean 105 and standard deviation 104. Among the factors influencing the rate is congestion, which produces alternating periods of faster and slower transmission. Let X represent the number of bytes downloaded in a randomly
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 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.a. If the car is small, what is the
A production facility contains two machines that are used to rework items that are initially defective. Let X be the number of hours that the first machine is in use, and let Y be the number of hours that the second machine is in use, on a randomly chosen day. Assume that X and Y have joint
The level of impurity (in percent) in the product of a certain chemical process is a random variable with probability density function.a. 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
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)
The following table presents the 100 senators of the 113th U.S. Congress on January 3, 2013, classified by political party affiliation and gender.A senator is selected at random from this group. Compute the following probabilities.a. The senator is a male Republican.b. The senator is a Democrat or
The main bearing clearance (in mm) in a certain type of engine is a random variable with probability density functiona. What is the probability that the clearance is less than 0.02 mm?b. Find the mean clearance.c. Find the standard deviation of the clearances.d. Find the cumulative distribution
A flywheel is attached to a crankshaft by 12 bolts, numbered 1 through 12. 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
Refer to Exercise 19.a. Find Î¼X.b. Find Î¼Y.c. Find ÏƒX.d. Find ÏƒY.e. Find Cov(X,Y).f. Find ÏX,Y.Refer to Exercise 19. Tensile Strength Concentration of Additive 100 150 200 0.02 0.05 0.06 0.11 0.04 0.01 0.08 0.10 0.06 0.04 0.08 0.17 0.08
An automobile insurance company divides customers into three categories, good risks, medium risks, and poor risks. Assume that 70% of the customers are good risks, 20% are medium risks, and 10% are poor risks. Assume that during the course of a year, a good risk customer has probability 0.005 of
The error in the length of a part (absolute value of the difference between the actual length and the target length), in mm, is a random variable with probability density function.a. What is the probability that the error is less than 0.2 mm?b. Find the mean error.c. Find the variance of the
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
A certain plant runs three shifts per day. Of all the items produced by the plant, 50% of them are produced on the first shift, 30% on the second shift, and 20% on the third shift. Of all the items produced on the first shift, 1% are defective, while 2% of the items produced on the second shift and
Refer to Exercise 21. Is it possible for the probability that both gauges fail to be greater than 0.01? Explain.Refer to Exercise 21.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
Here are two random variables that are uncorrelated but not independent. Let X and Y have the following joint probability mass function:a. Use the definition of independence on page 141 to show that X and Y are not independent (in factY = |X|, so Y is actually a function of X). b. Show that X
Refer to Exercise 23. Assume that the probabilities that each of the three scenarios occurs are P(A) = 0.20, P(B) = 0.30, and P(C) = 0.50.a. Find the probability that scenario A occurs and that the loss is 5%.b. Find the probability that the loss is 5%.c. Find the probability that scenario A occurs
The height H and radius R (in cm) of a cylindrical can are random with joint probability density function.The volume of a can is V = Ï€ R2H. Find Î¼V . 19 < h < 21 and 3(h – 20)²(r – 5) f (h, r) = 5
In a lot of n components, 30% 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. For which lot size n will A and B be more nearly independent: n = 10 or n
The diameter of a rivet (in mm) is a random variable with probability density function.a. What is the probability that the diameter is less than 12.5 mm?b. Find the mean diameter.c. Find the standard deviation of the diameters.d. Find the cumulative distribution function of the diameter.e. The
A stock solution of hydrochloric acid (HCl) supplied by a certain vendor contains small amounts of several impurities, including copper and nickel. Let X denote the amount of copper and let Y denote the amount of nickel, in parts per ten million, in a randomly selected bottle of solution. Assume
A fair coin is tossed five times. Which sequence ismore likely, HTTHH or HHHHH? Or are they equally likely? Explain.
Items are inspected for flaws by two quality inspectors. If a flaw is present, it will be detected by the first inspector with probability 0.9, and by the second inspector with probability 0.7. Assume the inspectors function independently.a. If an item has a flaw, what is the probability that it
Let X, Y, and Z be jointly distributed random variables. Prove that Cov(X + Y, Z) = Cov(X, Z) +Cov(Y, Z).
Two fair dice are rolled. Let X represent the number on the first die, and let Y represent the number on the second die. Find μXY .
Refer to Exercise 31. Assume the first card is not replaced before the second card is drawn.a. Find the joint probability mass function of X and Y.b. Find the marginal probability mass functions pX (x) and pY (y).c. Find μX and μY.d. Find μXY.e. Find Cov(X,Y ).Refer to Exercise 31.A box contains
A quality-control program at a plastic bottle production line involves inspecting finished bottles for flaws such as microscopic holes. The proportion of bottles that actually have such a flaw is only 0.0002. If a bottle has a flaw, the probability is 0.995 that it will fail the inspection. If a
Let X and Y be jointly continuous with joint probability density function f (x, y) and marginal densities fX (x) and fY (y). Suppose that f (x, y) = g(x)h(y) where g(x) is a function of x alone, h(y) is a function of y alone, and both g(x) and h(y) are nonnegative.a. Show that there exists a
Refer to Example 2.26. 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
A circle is drawn with radius R, where μR = 10 and σ2R = 1. The area of the circle is A = πR2. Find μA.
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
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.
Refer to Exercise 15. 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.Refer to Exercise 15. Lot Conforming Nonconforming 12 35 40 88 A B. 165 260
A closet contains four pairs of shoes. If four shoes are chosen at random, what is the probability that the chosen shoes do not contain a pair?
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?
The thickness X of a wooden shim (in mm) has probability density function.a. Find Î¼X.b. Find Ïƒ2X.c. Let Y denote the thickness of a shim in inches (1 mm = 0.0394 inches). Find Î¼Y and Ïƒ2Y.d. If three shims are selected independently and stacked one
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
Refer to 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). Refer to Exercise 12. y 1 2 3 0.13 0.10 0.07
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
The oxygen equivalence number of a weld is a number that can be used to predict properties such as hardness, strength, and ductility. The article “Advances in Oxygen Equivalence Equations for Predicting the Properties of Titanium Welds” (D. Harwig, W. Ittiwattana, and H. Castner, The Welding
Elongation (in percent) of steel plates treated with aluminum are random with probability density function.a. 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 deviation of the elongations.e.
Refer to Exercise 12. Assume that the cost of an engine repair is $50, and the cost of a transmission repair is $100. Let T represent the total cost of repairs during a one-hour time interval. a. Find μT. b. Find σT. c. Find P(T = 250). Refer to Exercise 12. y 1 2 3 0.13 0.10 0.07 0.03 1 0.12
Laura and Philip each fire one shot at a target. Laura has probability 0.5 of hitting the target, and Philip has probability 0.3. The shots are independent.a. Find the probability that the target is hit.b. Find the probability that the target is hit by exactly one shot.c. Given that the target was
The article “Traps in Mineral Valuations—Proceed With Care” (W. Lonegan, Journal of the Australasian Institute of Mining and Metallurgy, 2001:18–22) models the value (in millions of dollars) of a mineral deposit yet to be mined as a random variable X with probability mass function p(x)
In the article €œAn 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
Refer to Exercise 12. Let Z = X + Y represent the total number of repairs needed. a. Find μZ. b. Find σZ. c. Find P(Z = 2). Refer to Exercise 12. y 1 2 3 0.13 0.10 0.07 0.03 1 0.12 0.16 0.08 0.04 2 0.02 0.06 0.08 0.04 3 0.01 0.02 0.02 0.02
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
The Needleman-Wunsch method for aligning DNA sequences assigns 1 point whenever a mismatch occurs, and 3 points whenever a gap (insertion or deletion) appears in a sequence. Assume that under certain conditions, the number of mismatches has mean 5 and standard deviation 2, and the number of gaps
A drawer contains 6 red socks, 4 green socks, and 2 black socks. Two socks are chosen at random. What is the probability that they match?
Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passes the test, a success (S) occurs; if it fails the test, a failure (F) occurs. Assume that 80% of the components in the lot will succeed in passing the test. Let X
Automobile engines and transmissions are produced on assembly lines, and are inspected for defects after they come off their assembly lines. Those with defects are repaired. Let X represent the number of engines, and Y the number of transmissions that require repairs in a one-hour time interval.
Sarah and Thomas are going bowling. The probability that Sarah scores more than 175 is 0.4, and the probability that Thomas scores more than 175 is 0.2. Their scores are independent.a. Find the probability that both score more than 175.b. Given that Thomas scores more than 175, the probability that
Let A and B be events with P(A) = 0.3 and P(A ∪ B) = 0.7.a. For what value of P(B) will A and B be mutually exclusive?b. For what value of P(B) will A and B be independent?
A certain commercial jet plane uses a mean of 0.15 gallons of fuel per passenger-mile, with a standard deviation of 0.01 gallons.a. Find the mean number of gallons the plane uses to fly 8000 miles if it carries 210 passengers.b. Assume the amounts of fuel used are independent for each
A quality-control engineer samples 100 items manufactured by a certain process, and finds that 15 of them are defective. True or false:a. The probability that an item produced by this process is defective is 0.15.b. The probability that an item produced by this process is defective is likely to be
Refer to Exercise 10. Let Y be the number of chips tested up to and including the second acceptable chip.a. What is the smallest possible value for Y ?b. What is the probability that Y takes on that value?c. Let X represent the number of chips that are tested up to and including the first
The article “High Cumulative Risk of Lung Cancer Death among Smokers and Nonsmokers” (P. Brennan, et al. American Journal of Epidemiology, 2006:1233–1241) states that the probability is 0.24 that a man who is a heavy smoker will contract lung cancer. True or false:a. In a sample of 100 men
A gas station earns $2.60 in revenue for each gallon of regular gas it sells, $2.75 for each gallon of midgrade gas, and $2.90 for each gallon of premium gas. Let X1, X2, and X3 denote the numbers of gallons of regular, midgrade, and premium gasoline sold in a day. Assume that X1, X2, and X3 have
A company has hired 15 new employees, and must assign 6 to the day shift, 5 to the graveyard shift, and 4 to the night shift. In how many ways can the assignment be made?
Microprocessing chips are randomly sampled one by one from a large population, and tested to determine if they are acceptable for a certain application. Ninety percent of the chips in the population are acceptable.a. What is the probability that the first chip chosen is acceptable?b. What is the
Of all failures of a certain type of computer hard drive, it is determined that in 20% of them only the sector containing the file allocation table is damaged, in 70% of them only nonessential sectors are damaged, and in 10% of the cases both the allocation sector and one or more nonessential
In a lot of 10 components, 2 are sampled at random for inspection. Assume that in fact exactly 2 of the 10 components in the lot are defective. Let X be the number of sampled components that are defective.a. Find P(X = 0).b. Find P(X = 1).c. Find P(X = 2).d. Find the probability mass function of
An automobile insurance company divides customers into three categories, good risks, medium risks, and poor risks. Assume that 70% of the customers are good risks, 20% are medium risks, and 10% are poor risks. As part of an audit, one customer is chosen at random.a. What is the probability that the
A machine that fills bottles with a beverage has a fill volume whose mean is 20.01 ounces, with a standard deviation of 0.02 ounces. A case consists of 24 bottles randomly sampled from the output of the machine.a. Find the mean of the total volume of the beverage in the case.b. Find the standard
In a certain state, license plates consist of three letters followed by three numbers. a. How many different license plates can be made?b. How many different license plates can be made in which no letter or number appears more than once?c. A license plate is chosen at random. What is the
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...............0.411.............. 0.722..............
The reading given by a thermometer calibrated in ice water (actual temperature 0°C) is a random variable with probability density functionwhere k is a constant.a. Find the value of k.b. What is the probability that the thermometer reads above 0°C?c. What is the probability that the reading
A test consists of 15 questions. Ten are true-false questions, and five are multiple-choice questions that have four choices each. A student must select an answer for each question. In how many ways can this be done?
Two independent measurements are made of the lifetime of a charmed strange meson. Each measurement has a standard deviation of 7 × 10−15 seconds. The lifetime of the meson is estimated by averaging the two measurements. What is the standard deviation of this estimate?

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