Question: Each multiple-choice question on an examhas

> In Problems 15.32–15.36 you developed multiple regression models to predict the fair market value of houses in Glen Cove, Roslyn, and Freeport. Now write a report based on the models you developed. Append all appropriate charts and statistical informatio

> In Problem 20.3, you developed a payoff table for building a small factory or a large factory for manufacturing designer jeans. Given the results of that problem, suppose that the probabilities of the demand are as follows: a. Determine the optimal act

> For the following payoff table, the probability of event 1 is 0.5, and the probability of event 2 is also 0.5: a. Determine the optimal action based on the maximax criterion. b. Determine the optimal action based on the maximin criterion. c. Compute th

> The random variable is the number of nonconforming solder connections on a printed circuit board with 1000 connections.

> Actual lengths of stay at a hospital’s emergency department in 2009 are shown in the following table (rounded to the nearest hour). Length of stay is the total of wait and service times. Some longer stays are also approximated as 15 hou

> The distribution of the time until a Web site changes is important to Web crawlers that search engines use to maintain current information about Web sites. The distribution of the time until change (in days) of a Web site is approximated in the following

> Consider the visits that result in leave without being seen (LWBS) at an emergency department in Example 2.6. Assume that people independently arrive for service at hospital l. a. What is the probability that the fifth visit is the first one to LWBS? b.

> Suppose that lesions are present at 5 sites among 50 in a patient. A biopsy selects 8 sites randomly (without replacement). a. What is the probability that lesions are present in at least one selected site? b. What is the probability that lesions are pre

> A utility company might offer electrical rates based on time-of-day consumption to decrease the peak demand in a day. Enough customers need to accept the plan for it to be successful. Suppose that among 50 major customers, 15 would accept the plan. The u

> Suppose that a healthcare provider selects 20 patients randomly (without replacement) from among 500 to evaluate adherence to a medication schedule. Suppose that 10% of the 500 patients fail to adhere with the schedule. Determine the following: a. Probab

> a. For Exercise 3.7.1, calculate P(X = 1) and P(X = 4), assuming that X has a binomial distribution, and compare these results to results derived from the hypergeometric distribution. b. Use the binomial approximation to the hypergeometric distribution t

> A slitter assembly contains 48 blades. Five blades are selected at random and evaluated each day for sharpness. If any dull blade is found, the assembly is replaced with a newly sharpened set of blades. a. If 10 of the blades in an assembly are dull, wha

> A state runs a lottery in which six numbers are randomly selected from 40 without replacement. A player chooses six numbers before the state’s sample is selected. a. What is the probability that the six numbers chosen by a player match all six numbers in

> The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.05 flaw per square foot of plastic panel. Assume that an automobile interior contains 10 square feet of plastic panel. a. What i

> The analysis of results from a leaf transmutation experiment (turning a leaf into a petal) is summarized by the type of transformation completed: A naturalist randomly selects three leaves from this set without replacement. Determine the following proba

> Printed circuit cards are placed in a functional test after being populated with semiconductor chips. A lot contains 140 cards, and 20 are selected without replacement for functional testing. a. If 20 cards are defective, what is the probability that at

> A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure. a. If 10 men are selected randomly and tested for the marker, what is the probability that

> Suppose that X has a hypergeometric distribution with N = 10, n = 3, and K = 4. Sketch the probability mass function of X. Determine the cumulative distribution function for X.

> Suppose that X has a hypergeometric distribution with N = 100, n = 4, and K = 20. Determine the following: a. P(X = 1) b. P(X = 6) c. P(X = 4) d. Mean and variance of X

> A Web site randomly selects among 10 products to discount each day. The color printer of interest to you is discounted today. a. What is the expected number of days until this product is again discounted? b. What is the probability that this product is f

> In the process of meiosis, a single parent diploid cell goes through eight different phases. However, only 60% of the processes pass the first six phases and only 40% pass all eight. Assume that the results from each phase are independent. a. If the prob

> A trading company uses eight computers to trade on the New York Stock Exchange (NYSE). The probability of a computer failing in a day is 0.005, and the computers fail independently. Computers are repaired in the evening, and each day is an independent tr

> Assume that 20 parts are checked each hour and that X denotes the number of parts in the sample of 20 that require rework. Parts are assumed to be independent with respect to rework. a. If the percentage of parts that require rework remains at 1%, what i

> Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial blockage, disease, and infection. Assume that causes of he

> The number of views of a page on a Web site follows a Poisson distribution with a mean of 1.5 per minute. a. What is the probability of no views in a minute? b. What is the probability of two or fewer views in 10 minutes? c. Does the answer to the previo

> A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Successwith any opponent is independent of previous encounters. Until defeated, the player continues to contest opponents. a. What is the

> Assume that each of your calls to a popular radio station has a probability of 0.02 of connecting, that is, of not obtaining a busy signal. Assume that your calls are independent. a. What is the probability that your first call that connects is your 10th

> In a clinical study, volunteers are tested for a gene that has been found to increase the risk for a disease. The probability that a person carries the gene is 0.1. People are assumed to be independent with respect to the gene. a. What is the probability

> Consider a sequence of independent Bernoulli trials with p = 0.2. a. What is the expected number of trials to obtain the first success? b. After the eighth success occurs, what is the expected number of trials to obtain the ninth success?

> Suppose that X is a negative binomial random variable with p = 0.2 and r = 4. Determine the following: a. E(X) b. P(X = 20) c. P(X = 19) d. P(X = 21) e. The most likely value for X

> Suppose that the random variable X has a geometric distribution with p = 0.5. Determine the following probabilities: a. P(X = 1) b. P(X = 4) c. P(X = 8) d. P(X ≤ 2) e. P(X > 2)

> Consider the lengths of stay at a hospital’s emergency department in Exercise 3.1.19. Assume that five persons independently arrive for service. a. What is the probability that the length of stay of exactly one person is less than or equal to 4 hours? b.

> This exercise illustrates that poor quality can affect schedules and costs. A manufacturing process has 100 customer orders to fill. Each order requires one component part that is purchased from a supplier. However, typically, 2% of the components are id

> Because all airline passengers do not show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a passenger does not show up is 0.10, and the passengers behave independently. a. What i

> Samples of 20 parts from a metal punching process are selected every hour. Typically, 1% of the parts require rework. Let X denote the number of parts in the sample of 20 that require rework. A process problem is suspected if X exceeds its mean by more t

> In 1898, L. J. Bortkiewicz published a book titled The Law of Small Numbers. He used data collected over 20 years to show that the number of soldiers killed by horse kicks each year in each corps in the Prussian cavalry followed a Poisson distribution wi

> A computer system uses passwords that are exactly six characters and each character is one of the 26 letters (a–z) or 10 integers (0–9). Suppose that 10,000 users of the system have unique passwords. A hacker randomly selects (with replacement) 100,000 p

> Heart failure is due to either natural occurrences (87%) or outside factors (13%). Outside factors are related to induced substances or foreign objects. Natural occurrences are caused by arterial blockage, disease, and infection. Suppose that 20 patients

> Samples of rejuvenated mitochondria are mutated (defective) in 1% of cases. Suppose that 15 samples are studied and can be considered to be independent for mutation. Determine the following probabilities. a. No samples are mutated. b. At most one sample

> Amultiple-choice test contains 25 questions, each with four answers. Assume that a student just guesses on each question. a. What is the probability that the student answers more than 20 questions correctly? b. What is the probability that the student an

> An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is 0.01, and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the pro

> Determine the cumulative distribution function of a binomial random variable with n = 3 and p = 1/4.

> The random variable X has a binomial distribution with n = 10 and p = 0.5. Sketch the probability mass function of X. a. What value of X is most likely? b. What value(s) of X is(are) least likely? c. Repeat the previous parts with p = 0.01.

> The random variable X has a binomial distribution with n = 10 and p = 0.01. Determine the following probabilities. a. P(X = 5) b. P(X ≤ 2) c. P(X ≥ 9) d. P(3 ≤ X < 5)

> Let X be a binomial random variable with p = 0.1 and n = 10. Calculate the following probabilities. a. P(X ≤ 2) b. P(X > 8) c. P(X = 4) d. P(5 ≤ X ≤ 7)

> The number of cracks in a section of interstate highway that are significant enough to require repair is assumed to follow a Poisson distribution with a mean of two cracks per mile. a. What is the probability that there are no cracks that require repair

> For each scenario (a)–(j), state whether or not the binomial distribution is a reasonable model for the random variable and why. State any assumptions you make. a. A production process produces thousands of temperature transducers. Let X denote the numbe

> Trees are subjected to different levels of carbon dioxide atmosphere with 6% of them in a minimal growth condition at 350 parts per million (ppm), 10% at 450 ppm (slow growth), 47% at 550 ppm (moderate growth), and 37% at 650 ppm (rapid growth). What are

> The range of the random variable X is [0, 1, 2, 3, x] where x is unknown. If each value is equally likely and the mean of X is 6, determine x.

> Suppose that 1000 seven-digit telephone numbers within your area code are dialed randomly. What is the probability that your number is called?

> Thickness measurements of a coating process are made to the nearest hundredth of amillimeter. The thickness measurements are uniformly distributed with values 0.15, 0.16, 0.17, 0.18, and 0.19. Determine the mean and variance of the coating thickness for

> Suppose that X has a discrete uniform distribution on the integers 0 through 9. Determine the mean, variance, and standard deviation of the random variable Y = 5X and compare to the corresponding results for X.

> Let the random variable X have a discrete uniform distribution on the integers 0 ≤ x ≤ 99. Determine the mean and variance of X.

> Assume that the wavelengths of photosynthetically active radiations (PAR) are uniformly distributed at integer nanometers in the red spectrum from 675 to 700 nm. a. What are the mean and variance of the wavelength distribution for this radiation? b. If t

> An assembly consists of threemechanical components. Suppose that the probabilities that the first, second, and third components meet specifications are 0.95, 0.98, and 0.99, respectively. Assume that the components are independent. Determine the probabil

> Astronomers treat the number of stars in a given volume of space as a Poisson random variable. The density in theMilkyWay Galaxy in the vicinity of our solar system is one star per 16 cubic light-years. a. What is the probability of two or more stars in

> Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful with probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderatel

> In a semiconductor manufacturing process, three wafers from a lot are tested. Each wafer is classified as pass or fail. Assume that the probability that a wafer passes the test is 0.8 and that wafers are independent. Determine the probability mass functi

> An article in Knee Surgery, Sports Traumatology, Arthroscopy [“Arthroscopic Meniscal Repair with an Absorbable Screw: Results and Surgical Technique” (2005, Vol. 13, pp. 273–279)] cited a success rate of more than 90% for meniscal tears with a rim width

> a. P(X &acirc;&#137;&yen; 2) b. P(X c. P(X = 1.5) d. P(X 2.1)

> Consider the hospital patients in Example 2.6. Two patients are selected randomly, with replacement, from the total patients at Hospital 1. What is the probability mass function of the number of patients in the sample who are admitted?

> f (x) = 2x + 1 25 , x = 0, 1, 2, 3, 4 a. P(X = 4) b. P(X ≤ 1) c. P(2 ≤ X < 4) d. P(X > −10)

> f (x) = (8∕7)(1∕2)x , x = 1, 2, 3 a. P(X ≤ 1) b. P(X > 1) c. P(2 < X < 6) d. P(X ≤ 1 or X > 1)

> The sample space of a random experiment is {a, b, c, d, e, f }, and each outcome is equally likely. A random variable is defined as follows: Determine the probability mass function of X. Use the probability mass function to determine the following probab

> In a NiCd battery, a fully charged cell is composed of nickelic hydroxide. Nickel is an element that has multiple oxidation states. Assume the following proportions of the states: a. Determine the cumulative distribution function of the nickel charge. b.

> Determine the mean and variance of the random variable in Exercise 3.1.13.

> Data from www.centralhudsonlabs.com determined the mean number of insect fragments in 225-gram chocolate bars was 14.4, but three brands had insect contamination more than twice the average. See the U.S. Food and Drug Administration–Center for Food Safet

> Determine the mean and variance of the random variable in Exercise 3.1.12.

> Determine the mean and variance of the random variable in Exercise 3.1.11.

> Determine the mean and variance of the random variable in Exercise 3.1.10.

> It is suspected that some of the totes containing chemicals purchased from a supplier exceed the moisture content target. Assume that the totes are independent with respect to moisture content. Determine the proportion of totes from the supplier that mus

> Saguaro cacti are large cacti indigenous to the southwesternUnited States and Mexico.Assume that the number of saguaro cacti in a region follows a Poisson distribution with a mean of 280 per square kilometer. Determine the following: a. Mean number of ca

> An installation technician for a specialized communication system is dispatched to a city only when three or more orders have been placed. Suppose that orders follow a Poisson distribution with a mean of 0.25 per week for a city with a population of 100,

> From 500 customers, a major appliance manufacturer randomly selects a sample without replacement. The company estimates that 25% of the customers will reply to the survey. If this estimate is correct, what is the probability mass function of the number o

> Each main bearing cap in an engine contains 4 bolts. The bolts are selected at random without replacement froma parts bin that contains 30 bolts from one supplier and 70 bolts from another. a. What is the probability that a main bearing cap contains all

> Assume that the number of errors along a magnetic recording surface is a Poisson random variable with amean of one error every 105 bits. A sector of data consists of 4096 eight-bit bytes. a. What is the probability of more than one error in a sector? b.

> The random variable X has the following probability distribution: Determine the following: a. P(X &acirc;&#137;&curren; 3) b. P(X &gt; 2.5) c. P(2.7 d. E(X) e. V(X)

> Suppose that the number of customers who enter a store in an hour is a Poisson random variable, and suppose that P(X = 0) = 0.05. Determine the mean and variance of X.

> Determine the probability mass function for the random variable with the following cumulative distribution function:

> A manufacturer of a consumer electronics product expects 2% of units to fail during the warranty period. A sample of 500 independent units is tracked for warranty performance. a. What is the probability that none fails during thewarranty period? b. What

> In a manufacturing process that laminates several ceramic layers, 1% of the assemblies are defective. Assume that the assemblies are independent. a. What is the mean number of assemblies that need to be checked to obtain five defective assemblies? b. Wha

> Patient response to a generic drug to control pain is scored on a 5-point scale where a 5 indicates complete relief. Historically, the distribution of scores is Two patients, assumed to be independent, are each scored. a. What is the probability mass fun

> The probability that an individual recovers from an illness in a one-week time period without treatment is 0.1. Suppose that 20 independent individuals suffering from this illness are treated with a drug and 4 recover in a one-week time period. If the dr

> The number of errors in a textbook follows a Poisson distribution with a mean of 0.01 error per page. What is the probability that there are three or fewer errors in 100 pages?

> The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are independent. a. If you call 10 times, what is the probability that exactly nine of your calls are answered within 30 seconds? b. If y

> The number of messages that arrive at aWeb site is a Poisson random variable with a mean of five messages per hour. a. What is the probability that five messages are received in 1.0 hour? b. What is the probability that 10 messages are received in 1.5 ho

> Traffic flow is traditionally modeled as a Poisson distribution. A traffic engineer monitors the traffic flowing through an intersection with an average of six cars per minute. To set the timing of a traffic signal, the following probabilities are used.

> A shipment of chemicals arrives in 15 totes. Three of the totes are selected at random without replacement for an inspection of purity. If two of the totes do not conform to purity requirements, what is the probability that at least one of the nonconform

> The number of telephone calls that arrive at a phone exchange is often modeled as a Poisson random variable. Assume that on the average there are 10 calls per hour. Determine the following probabilities: a. exactly 5 calls in one hour b. 3 or fewer calls

> An electronic scale in an automated filling operation stops themanufacturing line after three underweight packages are detected. Suppose that the probability of an underweight package is 0.001 and each fill is independent. a. What is the mean number of f

> The probability that an eagle kills a rabbit in a day of hunting is 10%. Assume that results are independent for each day. a. What is the distribution of the number of days until a successful hunt? b. What is the probability that the first successful hu

> A particularly long traffic light on your morning commute is green on 20% of the mornings. Assume that each morning represents an independent trial. a. What is the probability that the first morning that the light is green is the fourth morning? b. What

> A congested computer network has a 1%chance of losing a data packet that must be resent, and packet losses are independent events. An e-mail message requires 100 packets. a. What is the distribution of the number of packets in an e-mail message that must

> An automated egg carton loader has a 1% probability of cracking an egg, and a customer will complain if more than one egg per dozen is cracked. Assume that each egg load is an independent event. a. What is the distribution of cracked eggs per dozen? Incl

> Let X denote the number of bits received in error in a digital communication channel, and assume that X is a binomial random variable with p = 0.001. If 1000 bits are transmitted, determine the following: a. P(X = 1) b. P(X ≥ 1) c. P(X ≤ 2) d. mean and

> Let the random variable X be equally likely to assume any of the values 1/8, 1/4, or 3/8. Determine the mean and variance of X.

> Consider the time to recharge the flash in cell-phone cameras as in Example 3.1. Assume that the probability that a camera passes the test is 0.8 and the cameras perform independently. What is the smallest sample size needed so that the probability of at

> The article “An Association Between Fine Particles and Asthma Emergency Department Visits for Children in Seattle” [Environmental Health Perspectives June 1999, Vol. 107(6)] used Poisson models for the number of asthma emergency department (ED) visits pe

> The probability that a visitor to aWeb site provides contact data for additional information is 0.01. Assume that 1000 visitors to the site behave independently. Determine the following probabilities: a. No visitor provides contact data. b. Exactly 10 vi

> An array of 30 LED bulbs is used in an automotive light. The probability that a bulb is defective is 0.001 and defective bulbs occur independently. Determine the following: a. Probability that an automotive light has two or more defective bulbs. b. Expec