 4.30E: Find the following percentiles for the standard normal distribution...
 4.101E: The completion time X for a certain task has cdf F(x) given by a. O...
 4.50E: In response to concerns about nutritional contents of fast foods, M...
 4.102E: Let X represent the number of individuals who respond to a particul...
 4.49E: Consider babies born in the “normal” range of 37–43 weeks gestation...
 4.103E: The article “Computer Assisted Net Weight Control” (Quality Progres...
 4.51E: Chebyshev’s inequality, (see Exercise 44, Chapter 3), is valid for ...
 4.104E: When circuit boards used in the manufacture of compact disc players...
 4.105E: Exercise 38 introduced two machines that produce wine corks, the fi...
 4.106E: The reaction time (in seconds) to a certain stimulus is a continuou...
 4.107E: Let X denote the temperature at which a certain chemical reaction t...
 4.108E:
 4.109E: The article “The Prediction of Corrosion by Statistical Analysis of...
 4.110E: Let t = the amount of sales tax a retailer owes the government for ...
 4.111E: The mode of a continuous distribution is the value x* that maximize...
 4.112E: The article “Error Distribution in Navigation” (J. of the Institute...
 4.113E:
 4.114E: Suppose a particular state allows individuals filing tax returns to...
 4.115E: Let be the input current to a transistor and I0 be the output curre...
 4.116E: The article “Response of SiCf/Si3N4 Composites UnderStatic and Cycl...
 4.117E: Let Z have a standard normal distribution and define a new rv Y by ...
 4.118E: a. Suppose the lifetime X of a component, when measured in hours, h...
 4.119E: In Exercises 117 and 118, as well as many other situations, one has...
 4.120E: Based on data from a dartthrowing experiment, the article “Shootin...
 4.121E: The article “Three Sisters Give Birth on the Same Day” (Chance, Spr...
 4.123E: Let U have a uniform distribution on the interval [0, 1]. Then obse...
 4.122E: Let X denote the lifetime of a component, with f(x) and F(x) the pd...
 4.124E: Consider an rv X with mean and standard deviation ?, and let g(X) b...
 4.125E: A function g(x) is convex if the chord connecting any two points on...
 4.126E: Let X have a Weibull distribution with parameters ? = 2 and . Show ...
 4.127E: An individual’s credit score is a number calculated based onthat pe...
 4.128E: Let V denote rainfall volume and W denote runoff volume (both in mm...
 4.10E: A family of pdf’s that has been used to approximate the distributio...
 4.11E: Let X denote the amount of time a book on twohour reserve is actua...
 4.31E: Determine z? for the following:a.? = .0055b.? = .09c.? = .663
 4.12E: The cdf for X ( = measurement error) of Exercise 3 is a. Compute P(...
 4.32E: Suppose the force acting on a column that helps to support a buildi...
 4.33E: Mopeds (small motorcycles with an engine capacity below50cm3 ) are ...
 4.52E: Let X denote the number of flaws along a 100m reel of magnetic tap...
 4.53E: Let X have a binomial distribution with parameters n =25 and p. Cal...
 4.54E: Suppose that 10% of all steel shafts produced by a certain process ...
 4.14E: The article “Modeling Sediment and Water Column Interactions for Hy...
 4.13E: Example 4.5 introduced the concept of time headway in traffic flow ...
 4.15E: Let X denote the amount of space occupied by an article placed in a...
 4.34E: The article “Reliability of DomesticWaste Biofilm Reactors” (J. of...
 4.35E: In a roadpaving process, asphalt mix is delivered to the hopper of...
 4.36E: Spray drift is a constant concern for pesticide applicators and agr...
 4.55E: Suppose only 75% of all drivers in a certain state regularly wear a...
 4.56E: Show that the relationship between a general normal percentile and ...
 4.57E: a. Show that if X has a normal distribution with parameters ? and ?...
 4.1E: The current in a certain circuit as measured by an ammeter is a con...
 4.2E: Suppose the reaction temperature X (in ?C) in a certain chemical pr...
 4.3E: The error involved in making a certain measurement is a continuous ...
 4.22E: The weekly demand for propane gas (in 1000s of gallons) from a part...
 4.23E: If the temperature at which a certain compound melts is a random va...
 4.24E: Let X have the Pareto pdf introduced in Exercise 10.a. If k>1, comp...
 4.43E: Vehicle speed on a particular bridge in China can k modeled as norm...
 4.44E: If bolt thread length is normally distributed, what is the probabil...
 4.45E: A machine that produces ball bearings has initially been set so tha...
 4.16E:
 4.17E:
 4.18E: Let X denote the voltage at the output of a microphone, and suppose...
 4.37E: Suppose that blood chloride concentration (mmol/L) has a normal dis...
 4.38E: There are two machines available for cutting corks intended for use...
 4.39E: The defect length of a corrosion defect in a pressurized steel pipe...
 4.58E: There is no nice formula for the standard normal cdf ?(z) , but sev...
 4.59E: Let X =the time between two successive arrivals at the driveup win...
 4.60E: Let X denote the distance (m) that an animal moves from its birth s...
 4.4E: Let X denote the vibratory stress (psi) on a wind turbine blade at ...
 4.5E: A college professor never finishes his lecture before the end of th...
 4.6E: The actual tracking weight of a stereo cartridge that is set to tra...
 4.25E: Let X be the temperature in °C at which a certain chemical reaction...
 4.26E: Let X be the total medical expenses (in 1000s of dollars)incurred b...
 4.27E: When a dart is thrown at a circular target, consider the location o...
 4.46E: The Rockwell hardness of a metal is determined by impressing a hard...
 4.47E: The weight distribution of parcels sent in a certain manner is norm...
 4.48E: Suppose Appendix Table A.3 contained ?(z) only for z ?0 Explain how...
 4.19E: Let X be a continuous rv with cdf [This type of cdf is suggested in...
 4.20E: Consider the pdf for total waiting time Y for two buses introduced ...
 4.21E: An ecologist wishes to mark off a circular sampling region having r...
 4.41E: The automatic opening device of a military cargo parachute has been...
 4.40E: The article “Monte Carlo Simulation—Tool for Better Understanding o...
 4.42E: The temperature reading from a thermocouple placed in a constantte...
 4.61E: Data collected at Toronto Pearson International Airport suggests th...
 4.62E: The paper “Microwave Observations of Daily Antarctic SeaIce Edge E...
 4.63E: A consumer is trying to decide between two longdistance calling pl...
 4.64E:
 4.65E: Let X denote the data transfer time(ms) in a grid computing system ...
 4.66E:
 4.67E: Suppose that when a transistor of a certain type is subjected to an...
 4.68E: The special case of the gamma distribution in which ? is a positive...
 4.69E: A system consists of five identical components connected in series ...
 4.70E: If X has an exponential distribution with parameter , derive a gene...
 4.71E: a. The event {X2 ?y} is equivalent to what event involving X itself...
 4.72E: The lifetime X (in hundreds of hours) of a certain type of vacuum t...
 4.73E: The authors of the article “A Probabilistic Insulation Life Model f...
 4.74E: Once an individual has been infected with a certain disease , let X...
 4.75E: Let X have a Weibull distribution with the pdf from Expression (4.1...
 4.76E: The article "The Statistics of Phytotoxic Air Pollutants" (J. of Ro...
 4.77E: The authors of the paper from which the data in Exercise 1.27 was e...
 4.78E: The article “On Assessing the Accuracy of Offshore Wind Turbine Rel...
 4.79E: Nonpoint source loads are chemical masses that travel to themain st...
 4.80E: a. Use Equation (4.13) to write a formula for the median of the log...
 4.81E: Sales delay is the elapsed time between the manufacture of a produc...
 4.82E: As in the case of the Weibull and Gamma distributions, the lognorma...
 4.83E: What condition on ? and ? is necessary for the standard beta pdf to...
 4.84E: Suppose the proportion X of surface area in a randomly selected qua...
 4.85E: Let X have a standard beta density with parameters ? and ?.a. Verif...
 4.86E: Stress is applied to a 20in. steel bar that is clamped in a fixed ...
 4.87E: The accompanying normal probability plot was constructed from a sam...
 4.88E: A sample of 15 female collegiate golfers was selected and the clubh...
 4.89E:
 4.90E: The article “A Probabilistic Model of Fracture in Concrete and Size...
 4.91E: Construct a normal probability plot for the fatiguecrack propagati...
 4.92E: The article “The LoadLife Relationship for M50 Bearings with Silic...
 4.94E: The accompanying observations are precipitation values during March...
 4.93E: Construct a probability plot that will allow you to assess the plau...
 4.95E: Use a statistical software package to construct a normal probabilit...
 4.7E: The article "Second Moment Reliability Evaluation vs. Monte Carlo S...
 4.96E: Let the ordered sample observations be denoted by y1, y2,….yn(y1 ( ...
 4.8E: In commuting to work, a professor must first get on a bus near her ...
 4.97E: The following failure time observations (1000s of hours) resulted f...
 4.9E:
 4.98E: Let X = the time it takes a read/write head to locate a desired rec...
 4.28E: Let Z be a standard normal random variable and calculate the follow...
 4.99E: A 12in. bar that is clamped at both ends is to be subjected to an ...
 4.29E: In each case, determine the value of the constant c that makes the ...
 4.100E: Let X denote the time to failure (in years) of a certain hydraulic ...
 4.98: Let X 5 the time it takes a read/write head to locate adesired reco...
 4.99: A 12in. bar that is clamped at both ends is to be subjectedto an i...
 4.100: Let X denote the time to failure (in years) of a certainhydraulic c...
 4.101: The completion time X for a certain task has cdf F(x)given by0 x , ...
 4.102: Let X represent the number of individuals who respondto a particula...
 4.103: The article Computer Assisted Net Weight Control(Quality Progress, ...
 4.104: When circuit boards used in the manufacture of compactdisc players ...
 4.105: Exercise 38 introduced two machines that produce winecorks, the fir...
 4.106: The reaction time (in seconds) to a certain stimulus is acontinuous...
 4.107: Let X denote the temperature at which a certain chemicalreaction ta...
 4.108: An oocyte is a female germ cell involved in reproduction.Based on a...
 4.109: The article The Prediction of Corrosion by StatisticalAnalysis of C...
 4.110: Let t = the amount of sales tax a retailer owes the governmentfor a...
 4.111: The mode of a continuous distribution is the value x* thatmaximizes...
 4.112: The article Error Distribution in Navigation (J. of theInstitute of...
 4.113: The article Statistical Behavior Modeling for DriverAdaptivePrecras...
 4.114: Suppose a particular state allows individuals filing taxreturns to ...
 4.115: Let Ii be the input current to a transistor and I0 be theoutput cur...
 4.116: The article Response of SiCf/Si3N4 Composites UnderStatic and Cycli...
 4.117: Let Z have a standard normal distribution and define anew rv Y by Y...
 4.118: a. Suppose the lifetime X of a component, when measuredin hours, ha...
 4.119: In Exercises 117 and 118, as well as many other situations,one has ...
 4.120: Based on data from a dartthrowing experiment, the articleShooting ...
 4.121: The article Three Sisters Give Birth on the SameDay (Chance, Spring...
 4.122: Let X denote the lifetime of a component, with f (x) andF(x) the pd...
 4.123: Let U have a uniform distribution on the interval [0, 1].Then obser...
 4.124: Consider an rv X with mean m and standard deviation s, andlet g(X) ...
 4.125: A function g(x) is convex if the chord connecting any twopoints on ...
 4.126: Let X have a Weibull distribution with parameters a 5 2and b. Show ...
 4.127: An individuals credit score is a number calculated basedon that per...
 4.128: Let V denote rainfall volume and W denote runoff volume(both in mm)...
Solutions for Chapter 4: Supplementary Exercises
Full solutions for Probability and Statistics for Engineering and the Sciences  9th Edition
ISBN: 9781305251809
Solutions for Chapter 4: Supplementary Exercises
Get Full SolutionsChapter 4: Supplementary Exercises includes 159 full stepbystep solutions. Since 159 problems in chapter 4: Supplementary Exercises have been answered, more than 98892 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineering and the Sciences, edition: 9. Probability and Statistics for Engineering and the Sciences was written by and is associated to the ISBN: 9781305251809.

Arithmetic mean
The arithmetic mean of a set of numbers x1 , x2 ,…, xn is their sum divided by the number of observations, or ( / )1 1 n xi t n ? = . The arithmetic mean is usually denoted by x , and is often called the average

Box plot (or box and whisker plot)
A graphical display of data in which the box contains the middle 50% of the data (the interquartile range) with the median dividing it, and the whiskers extend to the smallest and largest values (or some deined lower and upper limits).

C chart
An attribute control chart that plots the total number of defects per unit in a subgroup. Similar to a defectsperunit or U chart.

Central limit theorem
The simplest form of the central limit theorem states that the sum of n independently distributed random variables will tend to be normally distributed as n becomes large. It is a necessary and suficient condition that none of the variances of the individual random variables are large in comparison to their sum. There are more general forms of the central theorem that allow ininite variances and correlated random variables, and there is a multivariate version of the theorem.

Conditional probability density function
The probability density function of the conditional probability distribution of a continuous random variable.

Conidence interval
If it is possible to write a probability statement of the form PL U ( ) ? ? ? ? = ?1 where L and U are functions of only the sample data and ? is a parameter, then the interval between L and U is called a conidence interval (or a 100 1( )% ? ? conidence interval). The interpretation is that a statement that the parameter ? lies in this interval will be true 100 1( )% ? ? of the times that such a statement is made

Contrast
A linear function of treatment means with coeficients that total zero. A contrast is a summary of treatment means that is of interest in an experiment.

Correlation coeficient
A dimensionless measure of the linear association between two variables, usually lying in the interval from ?1 to +1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables).

Correlation matrix
A square matrix that contains the correlations among a set of random variables, say, XX X 1 2 k , ,…, . The main diagonal elements of the matrix are unity and the offdiagonal elements rij are the correlations between Xi and Xj .

Deining relation
A subset of effects in a fractional factorial design that deine the aliases in the design.

Distribution free method(s)
Any method of inference (hypothesis testing or conidence interval construction) that does not depend on the form of the underlying distribution of the observations. Sometimes called nonparametric method(s).

Eficiency
A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more eficient than another estimator if it has smaller variance. When estimators are biased, the concept requires modiication.

Enumerative study
A study in which a sample from a population is used to make inference to the population. See Analytic study

Error mean square
The error sum of squares divided by its number of degrees of freedom.

Estimate (or point estimate)
The numerical value of a point estimator.

Event
A subset of a sample space.

Expected value
The expected value of a random variable X is its longterm average or mean value. In the continuous case, the expected value of X is E X xf x dx ( ) = ?? ( ) ? ? where f ( ) x is the density function of the random variable X.

Firstorder model
A model that contains only irstorder terms. For example, the irstorder response surface model in two variables is y xx = + ?? ? ? 0 11 2 2 + + . A irstorder model is also called a main effects model

Fixed factor (or fixed effect).
In analysis of variance, a factor or effect is considered ixed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to it a model to the data for interpolating between these levels.

Geometric random variable
A discrete random variable that is the number of Bernoulli trials until a success occurs.