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Statistics For Business And Economics 8th Edition Paul Newbold, William Carlson, Betty Thorne - Solutions

A furniture manufacturer has found that the time spent by workers assembling a particular table follows a normal distribution with a mean of 150 minutes and a standard deviation of 40 minutes.a. The probability is 0.9 that a randomly chosen table requires more than how many minutes to assemble?b.
A company services copiers. A review of its records shows that the time taken for a service call can be represented by a normal random variable with a mean of 75 minutes and a standard deviation of 20 minutes.a. What proportion of service calls takes less than 1 hour?b. What proportion of service
Scores on an achievement test are known to be normally distributed with a mean of 420 and a standard deviation of 80.a. For a randomly chosen person taking this test, what is the probability of a score between 400 and 480?b. What is the minimum test score needed in order to be in the top 10% of all
It is estimated that the time that a well-known rock band, the Living Ingrates, spends on stage at its concerts follows a normal distribution with a mean of 200 minutes and a standard deviation of 20 minutes.a. What proportion of concerts played by this band lasts between 180 and 200 minutes?b. An
The daily selling price per 100 pounds of buffalo meat is normally distributed with a mean of $70, and the probability that the daily price is less than $85 is 0.9332. Four days are chosen at random. What is the probability that at least one of the days has a price that exceeds $80?
Given a random sample size of n = 900 from a binomial probability distribution with P = 0.50 do the following:a. Find the probability that the number of successes is greater than 500.b. Find the probability that the number of successes is fewer than 430.c. Find the probability that the number of
Given a random sample size of n = 1, 600 from a binomial probability distribution with P = 0.40, do the following:a. Find the probability that the number of successes is greater than 1,650.b. Find the probability that the number of successes is fewer than 1,530.c. Find the probability that the
Given a random sample size of n = 900 from a binomial probability distribution with P = 0.10 do the following:a. Find the probability that the number of successes is greater than 110.b. Find the probability that the number of successes is fewer than 53.c. Find the probability that the number of
Given a random sample size of n = 1, 600 from a binomial probability distribution with P = 0.40 do the following:a. Find the probability that the percentage of successes is greater than 0.45.b. Find the probability that the percentage of successes is less than 0.35.c. Find the probability that the
Given a random sample size of n = 400 from a binomial probability distribution with P = 0.20 do the following:a. Find the probability that the percentage of successes is greater than 0.25.b. Find the probability that the percentage of successes is less than 0.15.c. Find the probability that the
A car-rental company has determined that the probability a car will need service work in any given month is 0.2. The company has 900 cars.a. What is the probability that more than 200 cars will require service work in a particular month?b. What is the probability that fewer than 175 cars will need
It is known that 10% of all the items produced by a particular manufacturing process are defective. From the very large output of a single day, 400 items are selected at random.a. What is the probability that at least 35 of the selected items are defective?b. What is the probability that between 40
A random sample of 100 blue-collar employees at a large corporation are surveyed to assess their attitudes toward a proposed new work schedule. If 60% of all blue-collar employees at this corporation favor the new schedule, what is the probability that fewer than 50 in the random sample will be in
A hospital finds that 25% of its accounts are at least 1 month in arrears. A random sample of 450 accounts was taken.a. What is the probability that fewer than 100 accounts in the sample were at least 1 month in arrears?b. What is the probability that the number of accounts in the sample at least 1
The tread life of Stone Soup tires can be modeled by a normal distribution with a mean of 35,000 miles and a standard deviation of 4,000 miles. A sample of 100 of these tires is taken. What is the probability that more than 25 of them have tread lives of more than 38,000 miles?
Bags of a chemical produced by a company have impurity weights that can be represented by a normal distribution with a mean of 12.2 grams and a standard deviation of 2.8 grams. A random sample of 400 of these bags is taken. What is the probability that at least 100 of them contain fewer than 10
An analyst has available two forecasts, F1 and F2, of earnings per share of a corporation next year. He intends to form a compromise forecast as a weighted average of the two individual forecasts. In forming the compromise forecast, weight X will be given to the first forecast and weight (1
Given an arrival process with l = 1.0, what is the probability that an arrival occurs in the first t = 2 time units?
Given an arrival process with l = 8.0, what is the probability that an arrival occurs in the first t = 7 time units?
Given an arrival process with l = 5.0, what is the probability that an arrival occurs after t = 7 time units?
Given an arrival process with l = 5.0, what is the probability that an arrival occurs after t = 5 time units?
Given an arrival process with l = 3.0, what is the probability that an arrival occurs in the first t = 2 time units?
A professor sees students during regular office hours.Time spent with students follows an exponential distribution with a mean of 10 minutes.a. Find the probability that a given student spends fewer than 20 minutes with the professor.b. Find the probability that a given student spends more than 5
Suppose that the time between successive occurrences of an event follows an exponential distribution with a mean of 1/λ minutes. Assume that an event occurs.a. Show that the probability that more than 3 minutes elapses before the occurrence of the next event is e –3λ.b. Show that the
Swapna David is a customer assistant consultant for Acme Information Systems, who provides assistance for computer users. The mean number of calls per hour is 40 from across the United States and calls are independent.She has just finished a call and is scheduled to take the next call. What is the
The jurisdiction of a rescue team includes emergencies occurring on a stretch of river that is 4 miles long. Experience has shown that the distance along this stretch, measured in miles from its northernmost point, at which an emergency occurs can be represented by a uniformly distributed random
Delivery trucks arrive independently at the Floorstore Regional distribution center with various consumer items from the company's suppliers. The mean number of trucks arriving per hour is 20. Given that a truck has just arrived answer the following: a. What is the probability that the next truck
A random variable X is normally distributed with a mean of 100 and a variance of 100 and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable:W = 5X +
A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to -0.5. Find the mean and variance of the random variable:W = 5X
A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable:W = 5X
A random variable X is normally distributed with a mean of 500 and a variance of 100 and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to 0.5. Find the mean and variance of the random variable:W = 5X -
A random variable X is normally distributed with a mean of 100 and a variance of 500 and a random variable Y is normally distributed with a mean of 200 and a variance of 400. The random variables have a correlation coefficient equal to -0.5. Find the mean and variance of the random variable:W = 5X
An investor plans to divide $200,000 between two investments. The first yields a certain profit of 10%, whereas the second yields a profit with expected value 18% and standard deviation 6%. If the investor divides the money equally between these two investments, find the mean and standard deviation
A homeowner has installed a new energy-efficient furnace. It is estimated that over a year the new furnace will reduce energy costs by an amount that can be regarded as a random variable with a mean of $200 and a standard deviation of $60. Stating any assumptions you need to make, find the mean and
A consultant is beginning work on three projects. The expected profits from these projects are $50,000, $72,000, and $40,000. The associated standard deviations are $10,000, $12,000, and $9,000. Assuming independence of outcomes, find the mean and standard deviation of the consultant's total profit
A consultant has three sources of income-from teaching short courses, from selling computer software, and from advising on projects. His expected annual incomes from these sources are $20,000, $25,000, and $15,000, and the respective standard deviations are $2,000, $5,000, and $4,000. Assuming
The incomes of all families in a particular suburb can be represented by a continuous random variable. It is known that the median income for all families in this suburb is $60,000 and that 40% of all families in the suburb have incomes above $72,000. a. For a randomly chosen family, what is the
Five inspectors are employed to check the quality of components produced on an assembly line. For each inspector the number of components that can be checked in a shift can be represented by a random variable with mean 120 and standard deviation 15. Let X represent the number of components checked
It is estimated that in normal highway driving, the number of miles that can be covered by automobiles of a particular model on 1 gallon of gasoline can be represented by a random variable with mean 28 and standard deviation 2.4. Sixteen of these cars, each with 1 gallon of gasoline, are driven
Shirley Johnson, portfolio manager, has asked you to analyze a newly acquired portfolio to determine its mean value and variability. The portfolio consists of 50 shares of Xylophone Music and 40 shares of Yankee Workshop. Analysis of past history indicates that the share price of Xylophone Music
Prairie Flower Cereal has annual sales revenue of $400,000,000. George Severn, a 58-year-old senior vice president, is responsible for production and sales of Nougy 93 Fruity cereal. Daily production in cases is normally distributed, with a mean of 100 and a variance of 625. Daily sales in cases
The nation of Olecarl, located in the South Pacific, has asked you to analyze international trade patterns. You first discover that each year it exports 10 units and imports 10 units of wonderful stuff. The price of exports is a random variable with a mean of 100 and a variance of 100. The price of
You have been asked to determine the probability that the contribution margin for a particular product line exceeds the fixed cost of $2,000. The total number of units sold is a normally distributed random variable with a mean of 400 and a variance of 900, X ~ N(400, 900). The selling price per
The nation of Waipo has recently created an economic development plan that includes expanded exports and imports. It has completed a series of extensive studies of the world economy and Waipo's economic capability, following Waipo's extensive 10-year educational-enhancement program. The resulting
A consultant knows that it will cost him $10,000 to fulfill a particular contract. The contract is to be put out for bids, and he believes that the lowest bid, excluding his own, can be represented by a distribution that is uniform between $8,000 and $20,000. Therefore, if the random variable X
The ages of a group of executives attending a convention are uniformly distributed between 35 and 65 years. If the random variable X denotes ages in years, the probability density function is as follows:a. Graph the probability density function for X.b. Find and graph the cumulative distribution
The random variable X has probability density function as follows:a. Graph the probability density function for X.b. Show that the density has the properties of a proper probability density function.c. Find the probability that X takes a value between 0.5 and 1.5.
At the beginning of winter, a homeowner estimates that the probability is 0.4 that his total heating bill for the three winter months will be less than $380. He also estimates that the probability is 0.6 that the total bill will be less than $460. a. What is the probability that the total bill will
An investor puts $2,000 into a deposit account with a fixed rate of return of 10% per year. A second sum of $1,000 is invested in a fund with an expected rate of return of 16% and a standard deviation of 8% per year.a. Find the expected value of the total amount of money this investor will have
A hamburger stand sells hamburgers for $1.45 each.Daily sales have a distribution with a mean of 530 and a standard deviation of 69.a. Find the mean daily total revenues from the sale of hamburgers.b. Find the standard deviation of total revenues from the sale of hamburgers.c. Daily costs (in
An analyst forecasts corporate earnings, and her record is evaluated by comparing actual earnings with predicted earnings. Define the following: actual earnings = predicted earnings + forecast error. If the predicted earnings and forecast error are independent of each other, show that the variance
Let X1 and X2 be a pair of random variables. Show that the covariance between the random variables Y1 = (X1 + X2) and Y2 = (X1 - X2) is 0 if and only if X1 and X2 have the same variance.
Grade point averages of students on a large campus follow a normal distribution with a mean of 2.6 and a standard deviation of 0.5.a. One student is chosen at random from this campus.What is the probability that this student has a grade point average higher than 3.0?b. One student is chosen at
A company services home air conditioners. It is known that times for service calls follow a normal distribution with a mean of 60 minutes and a standard deviation of 10 minutes.a. What is the probability that a single service call takes more than 65 minutes?b. What is the probability that a single
It has been found that times taken by people to complete a particular tax form follow a normal distribution with a mean of 100 minutes and a standard deviation of 30 minutes.a. What is the probability that a randomly chosen person takes less than 85 minutes to complete this form?b. What is the
A pizza delivery service delivers to a campus dormitory. Delivery times follow a normal distribution with a mean of 20 minutes and a standard deviation of 4 minutes.a. What is the probability that a delivery will take between 15 and 25 minutes?b. The service does not charge for the pizza if
A video-rental chain estimates that annual expenditures of members on rentals follow a normal distribution with a mean of $100. It was also found that 10% of all members spend more than $130 in a year. What percentage of members spends more than $140 in a year?
It is estimated that amounts of money spent on gasoline by customers at a gas station follow a normal distribution with a standard deviation of $2.50. It is also found that 10% of all customers spent more than $25.What percentage of customers spent less than $20?
The total cost for a production process is equal to $1,000 plus two times the number of units produced. The mean and variance for the number of units produced are 500 and 900, respectively. Find the mean and variance of the total cost.
A market research organization has found that 40% of all supermarket shoppers refuse to cooperate when questioned by its pollsters. If 1,000 shoppers are approached, what is the probability that fewer than 500 will refuse to cooperate?
An organization that gives regular seminars on sales motivation methods determines that 60% of its clients have attended previous seminars. From a sample of 400 clients what is the probability that more than half have attended previous seminars?
An ambulance service receives an average of 15 calls per day during the time period 6 p.m. to 6 a.m. for assistance. For any given day what is the probability that fewer than 10 calls will be received during the 12-hour period? What is the probability that more than 17 calls during the 12-hour
In a large department store a customer-complaints office handles an average of six complaints per hour about the quality of service. The distribution is Poisson.a. What is the probability that in any hour exactly six complaints will be received?b. What is the probability that more than 20 minutes
A Chicago radio station believes that 40% of its listeners are younger than 25 years of age. Six hundred listeners are chosen at random.a. If the station's belief is correct, what is the probability that more than 260 of these listeners are younger than 25?b. If the station's belief is correct, the
It is estimated that times to completion for major league baseball games follow a normal distribution with a mean of 132 minutes and a standard deviation of 12 minutes.a. What proportion of all games last between 120 minutes and 150 minutes?b. Thirty-three percent of all games last longer than how
A management consultant found that the amount of time per day spent by executives performing tasks that could be done equally well by subordinates followed a normal distribution with a mean of 2.4 hours.It was also found that 10% of executives spent over 3.5 hours per day on tasks of this type. For
Financial Managers, Inc., buys and sells a large number of stocks routinely for the various accounts that it manages. Portfolio manager Andrea Colson has asked for your assistance in the analysis of the Johnson Fund. A portion of this portfolio consists of 10 shares of stock A and 8 shares of stock
Financial Managers, Inc., buys and sells a large number of stocks routinely for the various accounts that it manages. Portfolio manager Sarah Bloom has asked for your assistance in the analysis of the Burde Fund.A portion of this portfolio consists of 10 shares of stock A and 8 shares of stock B.
Big Nail Construction Inc. is building a large, new student center for a famous Midwestern liberal arts college. During the project Christine Buildumbig, the project manager, requests that a pile of sand weighing between 138,000 pounds and 141,000 pounds be placed on the newly constructed driveway.
Suppose that you toss a pair of dice and write down the value of the faces from each die.a. What is the population distribution for one die?b. Determine the sampling distribution of the sample means obtained by tossing two dice.
The lifetimes of lightbulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 hours. The population distribution is normal. Suppose that you purchase nine bulbs, which can be regarded as a random sample from the manufacturer's output.a. What is the
The fuel consumption, in miles per gallon, of all cars of a particular model has a mean of 25 and a standard deviation of 2. The population distribution can be assumed to be normal. A random sample of these cars is taken.a. Find the probability that sample mean fuel consumption will be fewer than
The mean selling price of senior condominiums in Green Valley over a year was $215,000. The population standard deviation was $25,000. A random sample of 100 new unit sales was obtained.a. What is the probability that the sample mean selling price was more than $210,000?b. What is the probability
Candidates for employment at a city fire department are required to take a written aptitude test. Scores on this test are normally distributed with a mean of 280 and a standard deviation of 60. A random sample of nine test scores was taken.a. What is the standard error of the sample mean score?b.
A random sample of 16 junior managers in the offices of corporations in a large city center was taken to estimate average daily commuting time for all such managers. Suppose that the population times have a normal distribution with a mean of 87 minutes and a standard deviation of 22 minutes.a. What
A company produces breakfast cereal. The true mean weight of the contents of its cereal packages is 20 ounces, and the standard deviation is 0.6 ounce. The population distribution of weights is normal. Suppose that you purchase four packages, which can be regarded as a random sample of all those
Assume that the standard deviation of monthly rents paid by students in a particular town is $40. A random sample of 100 students was taken to estimate the mean monthly rent paid by the whole student population.a. What is the standard error of the sample mean monthly rent?b. What is the probability
The times spent studying by students in the week before final exams follows a normal distribution with standard deviation 8 hours. A random sample of four students was taken in order to estimate the mean study time for the population of all students.a. What is the probability that the sample mean
An industrial process produces batches of a chemical whose impurity levels follow a normal distribution with standard deviation 1.6 grams per 100 grams of chemical. A random sample of 100 batches is selected in order to estimate the population mean impurity level.a. The probability is 0.05 that the
The price-earnings ratios for all companies whose shares are traded on the New York Stock Exchange follow a normal distribution with a standard deviation of 3.8. A random sample of these companies is selected in order to estimate the population mean price-earnings ratio.a. How large a sample is
Suppose that you have a fair coin and you label the head side as 1 and the tail side as 0. a. Now, you are asked to flip the coin 2 times and write down the numerical value that results from each toss. Without actually flipping the coin, write down the sampling distribution of the sample means. b.
The number of hours spent studying by students on a large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours. A random sample of these students is taken to estimate the population mean number of hours studying.a. How large a sample is needed
Greenstone Coffee is experiencing financial pressures due to increased competition for its numerous urban coffee shops. Total sales revenue has dropped by 15% and the company wishes to establish a sales monitoring process to identify shops that are underperforming. Historically, the daily mean
In taking a sample of n observations from a population of N members, the variance of the sampling distribution of the sample means is as follows:They quantity (N - n) / (N - 1) is called the finite population correction factor.a. To get some feeling for possible magnitudes of the finite population
A town has 500 real estate agents. The mean value of the properties sold in a year by these agents is $800,000, and the standard deviation is $300,000. A random sample of 100 agents is selected, and the value of the properties they sold in a year is recorded.a. What is the standard error of the
An English literature course was taken by 250 students. Each member of a random sample of 50 of these students was asked to estimate the amount of time he or she spent on the previous week's assignment. Suppose that the population standard deviation is 30 minutes.a. What is the probability that the
For an audience of 600 people attending a concert, the average time on the journey to the concert was 32 minutes, and the standard deviation was 10 minutes. A random sample of 150 audience members was taken.a. What is the probability that the sample mean journey time was more than 31 minutes?b.
Suppose that we have a population with proportion P = 0.40 and a random sample of size n = 100 drawn from the population.a. What is the probability that the sample proportion is greater than 0.45?b. What is the probability that the sample proportion is less than 0.29?c. What is the probability that
Suppose that we have a population with proportion P = 0.25 and a random sample of size n = 200 drawn from the population.a. What is the probability that the sample proportion is greater than 0.31?b. What is the probability that the sample proportion is less than 0.14?c. What is the probability that
Suppose that we have a population with proportion P = 0.60 and a random sample of size n = 100 drawn from the population.a. What is the probability that the sample proportion is more than 0.66?b. What is the probability that the sample proportion is less than 0.48?c. What is the probability that
Suppose that we have a population with proportion P = 0.50 and a random sample of size n = 900 drawn from the population.a. What is the probability that the sample proportion is more than 0.52?b. What is the probability that the sample proportion is less than 0.46?c. What is the probability that
A population contains 6 million 0s and 4 million 1s. What is the approximate sampling distribution of the sample mean in each of the following cases?a. The sample size is n = 5b. The sample size is n = 100
In 1992, Canadians voted in a referendum on a new constitution. In the province of Quebec, 42.4% of those who voted were in favor of the new constitution. A random sample of 100 voters from the province was taken.a. What is the mean of the distribution of the sample proportion in favor of a new
According to the Internal Revenue Service, 75% of all tax returns lead to a refund. A random sample of 100 tax returns is taken.a. What is the mean of the distribution of the sample proportion of returns leading to refunds?b. What is the variance of the sample proportion?c. What is the standard
A record store owner finds that 20% of customers entering her store make a purchase. One morning 180 people, who can be regarded as a random sample of all customers, enter the store. a. What is the mean of the distribution of the sample proportion of customers making a purchase? b. What is the
An administrator for a large group of hospitals believes that of all patients 30% will generate bills that become at least 2 months overdue. A random sample of 200 patients is taken.a. What is the standard error of the sample proportion that will generate bills that become at least 2 months
A corporation receives 120 applications for positions from recent college graduates in business. Assuming that these applicants can be viewed as a random sample of all such graduates, what is the probability that between 35% and 45% of them are women if 40% of all recent college graduates in
A charity has found that 42% of all donors from last year will donate again this year. A random sample of 300 donors from last year was taken.a. What is the standard error of the sample proportion who will donate again this year?b. What is the probability that more than half of these sample members
A corporation is considering a new issue of convertible bonds. Management believes that the offer terms will be found attractive by 20% of all its current stockholders.Suppose that this belief is correct. A random sample of 130 current stockholders is taken.a. What is the standard error of the
A store has determined that 30% of all lawn mower purchasers will also purchase a service agreement. In 1 month 280 lawn mowers are sold to customers, who can be regarded as a random sample of all purchasers.a. What is the standard error of the sample proportion of those who will purchase a service

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