 2.1E: Four universities—1, 2, 3, and 4—are participating in a holiday bas...
 2.2.1: List the elements of each of the following sample spaces: (a) the s...
 2.2E: Suppose that vehicles taking a particular freeway exit can turn rig...
 2.2.2: Use the rule method to describe the sample space S consisting of al...
 2.3E: Three components are connected to form a system as shown in the acc...
 2.2.3: Which of the following events are equal? (a) A = {1,3}; (b) B = {x ...
 2.4E: Each of a sample of four home mortgages is classified as fixed rate...
 2.2.4: An experiment involves tossing a pair of dice, one green and one re...
 2.5E: A family consisting of three persons—?A, B, ?and ?C?—goes to a medi...
 2.2.5: An experiment consists of tossing a die and then ipping a coin once...
 2.6E: A college library has five copies of a certain text on reserve. Two...
 2.2.6: Two jurors are selected from 4 alternates to serve at a murder tria...
 2.7E: An academic department has just completed voting by secret ballot f...
 2.2.7: Four students are selected at random from a chemistry class and cla...
 2.8E: An engineering construction firm is currently working on power plan...
 2.2.8: For the sample space of Exercise 2.4, (a) list the elements corresp...
 2.9E: Use Venn diagrams to verify the following two relationships for any...
 2.2.9: For the sample space of Exercise 2.5, (a) list the elements corresp...
 2.10E: a?? n Example 2.10, identify three events that are mutually exclusi...
 2.2.10: An engineering rm is hired to determine if certain waterways in Vir...
 2.11E: A mutual fund company offers its customers a variety of funds: a mo...
 2.2.11: The resumes of two male applicants for a college teaching position ...
 2.12E: Consider randomly selecting a student at a certain university, and ...
 2.2.12: Exercise and diet are being studied as possible substitutes for med...
 2.13E: A computer consulting firm presently has bids out on three projects...
 2.2.13: Construct a Venn diagram to illustrate the possible intersections a...
 2.14E: Suppose that 55% of all adults regularly consume coffee, 45% regula...
 2.2.14: If S = {0,1,2,3,4,5,6,7,8,9} and A = {0,2,4,6,8}, B = {1,3,5,7,9}, ...
 2.15E: Consider the type of clothes dryer (gas or electric) purchased by e...
 2.2.15: Consider the sample space S ={copper, sodium, nitrogen, potassium, ...
 2.16E: An individual is presented with three different glasses of cola, la...
 2.2.16: If S = {x  0 <x<12}, M = {x  1 <x<9}, and N = {x  0 <x<5}, nd (a...
 2.17E: Let ?A ?denote the event that the next request for assistance from ...
 2.2.17: Let A, B, and C be events relative to the sample space S. Using Ven...
 2.18E: A wallet contains five $10 bills, four $5 bills, and six $1 bills (...
 2.2.18: Which of the following pairs of events are mutually exclusive? (a) ...
 2.19E: Human visual inspection of solder joints on printed circuit boards ...
 2.2.19: Suppose that a family is leaving on a summer vacation in their camp...
 2.20E: A certain factory operates three different shifts. Over the last ye...
 2.2.20: Referring to Exercise 2.19 and the Venn diagram of Figure 2.5, list...
 2.21E: An insurance company offers four different deductible levels—none, ...
 2.2.21: Registrants at a large convention are oered 6 sightseeing tours on ...
 2.22E: The route used by a certain motorist in commuting to work contains ...
 2.2.22: In a medical study, patients are classied in 8 ways according to wh...
 2.23E: The computers of six faculty members in a certain department are to...
 2.2.23: If an experiment consists of throwing a die and then drawing a lett...
 2.24E: Show that if one event ?A ?is contained in another event ?B ?(i.e.,...
 2.2.24: Students at a private liberal arts college are classied as being fr...
 2.25E: The three most popular options on a certain type of new car are a b...
 2.2.25: A certain brand of shoes comes in 5 dierent styles, with each style...
 2.26E: A certain system can experience three different types of defects. L...
 2.2.26: A California study concluded that following 7 simple health rules c...
 2.27E: An academic department with five faculty members—Anderson, Box, Cox...
 2.2.27: A developer of a new subdivision oers a prospective home buyer a ch...
 2.28E: In Exercise 5, suppose that any incoming individual is equally like...
 2.2.28: A drug for the relief of asthma can be purchased from 5 dierent man...
 2.29E: As of April 2006, roughly 50 million .com web domain names were reg...
 2.2.29: In a fuel economy study, each of 3 race cars is tested using 5 dier...
 2.30E: A friend of mine is giving a dinner party. His current wine supply ...
 2.2.30: In how many dierent ways can a truefalse test consisting of 9 ques...
 2.31E: The composer Beethoven wrote 9 symphonies, 5 piano concertos (music...
 2.2.31: A witness to a hitandrun accident told the police that the licens...
 2.32E: An electronics store is offering a special price on a complete set ...
 2.2.32: (a) In how many ways can 6 people be lined up to get on a bus? (b) ...
 2.33E: Again consider a Little League team that has 15 players on its rost...
 2.2.33: If a multiplechoice test consists of 5 questions, each with 4 poss...
 2.34E: Computer keyboard failures can be attributed to electrical defects ...
 2.2.34: (a) How many distinct permutations can be made from the letters of ...
 2.35E: A production facility employs 20 workers on the day shift, 15 worke...
 2.2.35: A contractor wishes to build 9 houses, each different in design. In...
 2.36E: An academic department with five faculty members narrowed its choic...
 2.2.36: (a) How many threedigit numbers can be formed from the digits 0, 1...
 2.37E: An experimenter is studying the effects of temperature, pressure, a...
 2.2.37: In how many ways can 4 boys and 5 girls sit in a row if the boys an...
 2.38E: A sonnet is a 14line poem in which certain rhyming patterns are fo...
 2.2.38: Four married couples have bought 8 seats in the same row for a conc...
 2.39E: A box in a supply room contains 15 compact fluorescent lightbulbs, ...
 2.2.39: In a regional spelling bee, the 8 nalists consist of 3 boys and 5 g...
 2.40E: Three molecules of type ?A, ?three of type ?B, ?three of type ?C, ?...
 2.2.40: In how many ways can 5 starting positions on a basketball team be l...
 2.41E: An ATM personal identification number (PIN) consists of four digits...
 2.2.41: Find the number of ways that 6 teachers can be assigned to 4 sectio...
 2.42E: A starting lineup in basketball consists of two guards, two forward...
 2.2.42: Three lottery tickets for rst, second, and third prizes are drawn f...
 2.43E: In fivecard poker, a straight consists of five cards with adjacent...
 2.2.43: In how many ways can 5 dierent trees be planted in a circle?
 2.44E: Show that . Give an interpretation involving subsets.
 2.2.44: In how many ways can a caravan of 8 covered wagons from Arizona be ...
 2.45E: The population of a particular country consists of three ethnic gro...
 2.2.45: How many distinct permutations can be made from the letters of the ...
 2.46E: Suppose an individual is randomly selected from the population of a...
 2.2.46: In how many ways can 3 oaks, 4 pines, and 2 maples be arranged alon...
 2.47E: 47E
 2.2.47: How many ways are there to select 3 candidates from 8 equally quali...
 2.48E: Reconsider the system defect situation described in Exercise 26 (Se...
 2.2.48: How many ways are there that no two students will have the same bir...
 2.49E: The accompanying table gives information on the type of coffee sele...
 2.2.49: Find the errors in each of the following statements: (a) The probab...
 2.50E: A department store sells sport shirts in three sizes (small, medium...
 2.2.50: Assuming that all elements of S in Exercise 2.8 on page 42 are equa...
 2.51E: According to a July 31, 2013, posting on cnn.com subsequent to the...
 2.2.51: A box contains 500 envelopes, of which 75 contain $100 in cash, 150...
 2.52E: A system consists of two identical pumps, #1 and #2. If one pump fa...
 2.2.52: Suppose that in a senior college class of 500 students it is found ...
 2.53E: A certain shop repairs both audio and video components. Let ?A ?den...
 2.2.53: The probability that an American industry will locate in Shanghai, ...
 2.54E: In Exercise 13, Ai={ awarded project i} , for I =1,2,3. Use the pro...
 2.2.54: it will locate in Beijing, China, is 0.4, and the probability that ...
 2.55E: Deer ticks can be carriers of either Lyme disease or human granuloc...
 2.2.55: If each coded item in a catalog begins with 3 distinct letters foll...
 2.56E: For any events ?A? nd ?B ?with P(B)>0, show that P(AB)+ P(A ’B)= 1
 2.2.56: An automobile manufacturer is concerned about a possible recall of ...
 2.57E: If P(BA)> P(B), show that P( B ’A) < P(B ’). [?Hint: ?Add P( B’A)...
 2.2.57: If a letter is chosen at random from the English alphabet, nd the p...
 2.58E: Show that for any three events ?A, B, ?and ?C ?with P(C) > 0, P(A ?...
 2.2.58: A pair of fair dice is tossed. Find the probability of getting (a) ...
 2.59E: At a certain gas station, 40% of the customers use regular gas (?A?...
 2.2.59: In a poker hand consisting of 5 cards, nd the probability of holdin...
 2.60E: Seventy percent of the light aircraft that disappear while in fligh...
 2.2.60: If 3 books are picked at random from a shelf containing 5 novels, 3...
 2.61E: Components of a certain type are shipped to a supplier in batches o...
 2.2.61: In a high school graduating class of 100 students, 54 studied mathe...
 2.62E: Blue Cab operates 15% of the taxis in a certain city, and Green Cab...
 2.2.62: Doms Pizza Company uses taste testing and statistical analysis of t...
 2.63E: For customers purchasing a refrigerator at a certain appliance stor...
 2.2.63: According to Consumer Digest (July/August 1996), the probable locat...
 2.64E: The Reviews editor for a certain scientific journal decides whether...
 2.2.64: Interest centers around the life of an electronic component. Suppos...
 2.65E: A large operator of timeshare complexes requires anyone interested ...
 2.2.65: Consider the situation of Exercise 2.64. Let A be the event that th...
 2.66E: Consider the following information about travelers on vacation (bas...
 2.2.66: Factory workers are constantly encouraged to practice zero toleranc...
 2.67E: There has been a great deal of controversy over the last several ye...
 2.2.67: Interest centers around the nature of an oven purchased at a partic...
 2.68E: A friend who lives in Los Angeles makes frequent consulting trips t...
 2.2.68: It is common in many industrial areas to use a lling machine to ll ...
 2.69E: In Exercise 59, consider the following additional information on cr...
 2.2.69: It is common in many industrial areas to use a lling machine to ll ...
 2.70E: Reconsider the credit card scenario of Exercise 47 (Section 2.4), a...
 2.2.70: Consider the situation of Exercise 2.69. Suppose 50,000 boxes of de...
 2.71E: An oil exploration company currently has two active projects, one i...
 2.2.71: As the situation of Exercise 2.69 might suggest, statistical proced...
 2.72E: In Exercise 13, is any ?A?i ?independent of any other ?A?j? Answer ...
 2.2.72: Prove that P(AB)=1+P(AB)P(A)P(B).
 2.73E: If ?A ?and ?B ?are independent events, show that ?A?_ and ?B ?are a...
 2.2.73: If R is the event that a convict committed armed robbery and D is t...
 2.74E: The proportions of blood phenotypes in the U.S. population are as f...
 2.2.74: A class in advanced physics is composed of 10 juniors, 30 seniors, ...
 2.75E: One of the assumptions underlying the theory of control charting (s...
 2.2.75: A random sample of 200 adults are classied below by sex and their l...
 2.76E: In October, 1994, a flaw in a certain Pentium chip installed in com...
 2.2.76: In an experiment to study the relationship of hypertension and smok...
 2.77E: An aircraft seam requires 25 rivets. The seam will have to be rewor...
 2.2.77: In the senior year of a high school graduating class of 100 student...
 2.78E: A boiler has five identical relief valves. The probability that any...
 2.2.78: A manufacturer of a u vaccine is concerned about the quality of its...
 2.79E: Two pumps connected in parallel fail independently of one another o...
 2.2.79: In USA Today (Sept. 5, 1996), the results of a survey involving the...
 2.80E: Consider the system of components connected as in the accompanying ...
 2.2.80: The probability that an automobile being lled with gasoline also ne...
 2.81E: Refer back to the seriesparallel system configuration introduced i...
 2.2.81: The probability that a married man watches a certain television sho...
 2.82E: Consider independently rolling two fair dice, one red and the other...
 2.2.82: For married couples living in a certain suburb, the probability tha...
 2.83E: Components arriving at a distributor are checked for defects by two...
 2.2.83: The probability that a vehicle entering the Luray Caverns has Canad...
 2.84E: Consider purchasing a system of audio components consisting of a re...
 2.2.84: The probability that the head of a household is home when a telemar...
 2.85E: A quality control inspector is inspecting newly produced items for ...
 2.2.85: The probability that a doctor correctly diagnoses a particular illn...
 2.86E: a. A lumber company has just taken delivery on a lot of 10, 002 × 4...
 2.2.86: In 1970, 11% of Americans completed four years of college; 43% of t...
 2.87E: Consider randomly selecting a single individual and having that per...
 2.2.87: A real estate agent has 8 master keys to open several new homes. On...
 2.89E: Suppose identical tags are placed on both the left ear and the righ...
 2.2.88: Before the distribution of certain statistical software, every four...
 2.90E: A certain legislative committee consists of 10 senators. A subcommi...
 2.2.89: A town has two re engines operating independently. The probability ...
 2.91E: A factory uses three production lines to manufacture cans of a cert...
 2.2.90: Pollution of the rivers in the United States has been a problem for...
 2.92E: An employee of the records office at a certain university currently...
 2.2.91: Find the probability of randomly selecting 4 good quarts of milk in...
 2.93E: One satellite is scheduled to be launched from Cape Canaveral in Fl...
 2.2.92: Suppose the diagram of an electrical system is as given in Figure 2...
 2.94E: A transmitter is sending a message by using a binary code, namely, ...
 2.2.93: A circuit system is given in Figure 2.11. Assume the components fai...
 2.95E: Individual A has a circle of five close friends (B, C, D, E, and F)...
 2.2.94: In the situation of Exercise 2.93, it is known that the system does...
 2.96E: According to the article “Optimization of Distribution Parameters f...
 2.2.95: In a certain region of the country it is known from past experience...
 2.97E: A chemical engineer is interested in determining whether a certain ...
 2.2.96: Police plan to enforce speed limits by using radar traps at four di...
 2.98E: Five friends—Allison, Beth, Carol, Diane, and Evelyn—have identical...
 2.2.97: Referring to Exercise 2.95, what is the probability that a person d...
 2.99E: Fasteners used in aircraft manufacturing are slightly crimped so th...
 2.2.98: If the person in Exercise 2.96 received a speeding ticket on her wa...
 2.100E: Jay and Maurice are playing a tennis match. In one particular game,...
 2.2.99: Suppose that the four inspectors at a lm factory are supposed to st...
 2.101E: A system consists of two components. The probability that the secon...
 2.2.100: A regional telephone company operates three identical relay station...
 2.102E: 102E
 2.2.101: A paintstore chain produces and sells latex and semigloss paint. B...
 2.103E: a. A certain company sends 40% of its overnight mail parcels via ex...
 2.2.102: Denote by A, B, and C the events that a grand prize is behind doors...
 2.104E: A company uses three different assembly lines—?A?1,?A?2, and ?A?3—t...
 2.2.103: A truth serum has the property that 90% of the guilty suspects are ...
 2.105E: Disregarding the possibility of a February 29 birthday, suppose a r...
 2.2.104: An allergist claims that 50% of the patients she tests are allergic...
 2.106E: One method used to distinguish between granitic (?G?) and basaltic ...
 2.2.105: By comparing appropriate regions of Venn diagrams, verify that (a) ...
 2.107E: A subject is allowed a sequence of glimpses to detect a target . Le...
 2.2.106: The probabilities that a service station will pump gas into 0, 1, 2...
 2.108E: In a Little League baseball game, team A’s pitcher throws a strike ...
 2.2.107: How many bridge hands are possible containing 4 spades, 6 diamonds,...
 2.109E: Four engineers, A, B, C, and D, have been scheduled for job intervi...
 2.2.108: If the probability is 0.1 that a person will make a mistake on his ...
 2.110E: A particular airline has 10 A.M. flights from Chicago to New York, ...
 2.2.109: A large industrial rm uses three local motels to provide overnight ...
 2.111E: A personnel manager is to interview four candidates for a job. Thes...
 2.2.110: The probability that a patient recovers from a delicate heart opera...
 2.112E: Consider four independent events ?A?1, ?A?2, ?A?3, and ?A?4, and le...
 2.2.111: In a certain federal prison, it is known that 2/3 of the inmates ar...
 2.113E: A box contains the following four slips of paper, each having exact...
 2.2.112: From 4 red, 5 green, and 6 yellow apples, how many selections of 9 ...
 2.114E: Show that if ?A?1, ?A?2, and ?A?3 are independent events, then ?P?(...
 2.2.113: From a box containing 6 black balls and 4 green balls, 3 balls are ...
 2.2.114: A shipment of 12 television sets contains 3 defective sets. In how ...
 2.2.115: A certain federal agency employs three consulting rms (A, B, and C)...
 2.2.116: A manufacturer is studying the eects of cooking temperature, cookin...
 2.2.117: Consider the situation in Exercise 2.116, and suppose that the manu...
 2.2.118: A certain form of cancer is known to be found in women over 60 with...
 2.2.119: A producer of a certain type of electronic component ships to suppl...
 2.2.120: A rare disease exists with which only 1 in 500 is aected. A test fo...
 2.2.121: A construction company employs two sales engineers. Engineer 1 does...
 2.2.122: In the eld of quality control, the science of statistics is often u...
 2.2.123: An industrial plant is conducting a study to determine how quickly ...
 2.2.124: A rm is accustomed to training operators who do certain tasks on a ...
 2.2.125: A survey of those using a particular statistical software system in...
 2.2.126: During bad economic times, industrial workers are dismissed and are...
 2.2.127: There is a 5050 chance that the queen carries the gene of hemophil...
 2.2.128: Group Project: Give each student a bag of chocolate M&Ms. Divide th...
Solutions for Chapter 2: Probability and Statistics for Engineers and the Scientists 9th Edition
Full solutions for Probability and Statistics for Engineers and the Scientists  9th Edition
ISBN: 9780321629111
Solutions for Chapter 2
Get Full SolutionsSince 241 problems in chapter 2 have been answered, more than 152019 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 2 includes 241 full stepbystep solutions. This textbook survival guide was created for the textbook: Probability and Statistics for Engineers and the Scientists, edition: 9. Probability and Statistics for Engineers and the Scientists was written by and is associated to the ISBN: 9780321629111.

Addition rule
A formula used to determine the probability of the union of two (or more) events from the probabilities of the events and their intersection(s).

Alias
In a fractional factorial experiment when certain factor effects cannot be estimated uniquely, they are said to be aliased.

Bivariate distribution
The joint probability distribution of two random variables.

Causal variable
When y fx = ( ) and y is considered to be caused by x, x is sometimes called a causal variable

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.

Completely randomized design (or experiment)
A type of experimental design in which the treatments or design factors are assigned to the experimental units in a random manner. In designed experiments, a completely randomized design results from running all of the treatment combinations in random order.

Confounding
When a factorial experiment is run in blocks and the blocks are too small to contain a complete replicate of the experiment, one can run a fraction of the replicate in each block, but this results in losing information on some effects. These effects are linked with or confounded with the blocks. In general, when two factors are varied such that their individual effects cannot be determined separately, their effects are said to be confounded.

Continuous random variable.
A random variable with an interval (either inite or ininite) of real numbers for its range.

Contour plot
A twodimensional graphic used for a bivariate probability density function that displays curves for which the probability density function is constant.

Correction factor
A term used for the quantity ( / )( ) 1 1 2 n xi i n ? = that is subtracted from xi i n 2 ? =1 to give the corrected sum of squares deined as (/ ) ( ) 1 1 2 n xx i x i n ? = i ? . The correction factor can also be written as nx 2 .

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 .

Curvilinear regression
An expression sometimes used for nonlinear regression models or polynomial regression models.

Decision interval
A parameter in a tabular CUSUM algorithm that is determined from a tradeoff between false alarms and the detection of assignable causes.

Error sum of squares
In analysis of variance, this is the portion of total variability that is due to the random component in the data. It is usually based on replication of observations at certain treatment combinations in the experiment. It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a modelitting process and not on replication.

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.

False alarm
A signal from a control chart when no assignable causes are present

Fraction defective control chart
See P chart

Generating function
A function that is used to determine properties of the probability distribution of a random variable. See Momentgenerating function

Harmonic mean
The harmonic mean of a set of data values is the reciprocal of the arithmetic mean of the reciprocals of the data values; that is, h n x i n i = ? ? ? ? ? = ? ? 1 1 1 1 g .