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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

The accounting firm of Price Waterhouse annually monitors the U.S. Postal Service's performance. One parameter of interest is the percentage of mail delivered on time. In a sample of 332,000 items
Family-owned companies are notorious for having difficulties in transferring control from one generation to the next. Part of this problem can be traced to lack of a well-documented strategic
Suppose you wish to estimate a population mean correct to within a bound B = .20 with probability equal to.90.You do not know a', but you know that the observations will range in value between 30 and
In each case, find the approximate sample size required to construct a 95% confidence interval for p that has bound B = .08.a. Assume p is near .2.b. Assume you have no prior knowledge about p, but
'Ihe following is a 90% confidence interval for p: (.26, S4). How large was the sample used to construct this interval?
Suppose you wish to estimate the mean of a normal population using a 95% confidence interval, and you know from prior information that a2 .-. 1.a. To see the effect of the sample size on the width of
Do you pay for certain Web services? Georgia Institute of Technology's Graphics Visualization and Usability Center surveyed 13,000 Internet users and asked them about their willingness to pay fees
In a survey conducted for Money magazine by the ICR Survey Research Group, 26% of parents with collegebound high school children reported not having saved any money for college. The poll had a ". . .
It costs more to produce defective items-since they must be scrapped or reworked-than it does to produce nondefective items. This simple fact suggests that manufacturers should ensure the quality of
Let t, represent a particular value of t from Table VI of Appendix B. Find the table values such that the follow11 ing statements arc true.a. P(t 5 t,) = .05 where df = 20b. P(t 2 to) = .005 where df
A random sample of 225 measurements is selected from a population, and the sample mean and standard deviation are 5 = 32.5 and s = 30.0, respectively.a. Use a 99% confidence interval to estimate the
In a random sample of 400 measurements, 227 of the measurements possess the characteristic of interest,A.a. Use a 95% confidence interval to estimate the true proportion p of measurements in the
As part of a study of residential property values in Cedar Grove, New Jersey, the county tax assessor sampled 20 single-family homes that sold during 1996 and recorded their sales prices (in
The Centers for Disease Control and Prevention(CDCP) in Atlanta, Georgia, conducts an annual survey of the general health of the US. population as part of its Behavioral Risk Factor Surveillance
Research reported in the Professional Geographer(May 1992) investigates the hypothesis that the disproportionate housework responsibility of women in twoincome households is a major factor in
Refer to the Journal of the American Medical Association (Apr. 21,1993) report on the prevalence of cigarette smoking among U.S. adults, Exercise 5.7(p. 266). Of the 43,732 survey respondents, 11,239
Refer to the National Highway Traffic Safety Administration (NHTSA) study of fatal auto accidents caused by air bags, Exercise 5.30(p. 285). Recall that the NHTSA wants to estimate the proportion of
Security analysts are professionals who devote full-time efforts to evaluating the investment worth of a narrow list of stocks. For example, one security analyst might specialize in bank stocks while
Give two examples of a business-oriented discrete random variable. Do the same for a continuous random variable.
Give an example of a continuous random variable that would be of interest to an economist.
Give an example of a discrete random variable that would be of interest to the manager of a hotel.
Give an example of a continuous random variable that would be of interest to a stockbroker.
A dl~crete random variable x can assume five possible I values: 2, 3, 5, 8, and 10. Its probability distribution isshown here:"a. What is p(5)?b. What is the probability that x equals 2 or lo?c. What
Explain why each of the following is or is not a valid probability distribution for a discrete random variable x:a. x 0123
The random variable x has the following discrete probability distribution:a. Find P(x 5 3).b. Find P(x < 3).c. Find P(x = 7).d. Find P(x 2 5).e. Find P(x > 2).f. Find P(3 % x 5 9).
Consider the probability distribution shown here.a. Find p = E(x).b. Find u2 = E[(x - p)'].c. Find u.d. Interpret the value you obtained for p.e. In this case, can the random variable x ever assume
Consider the probability distribution for the random variable x shown at the top of the next column.a. Find p, u2, and a.b. Graphp(x).c. Locate p and the interval p f 2u on your graph.What is the
The age distribution as of July 1, 1999 for the 55 employees of a highly successful two-year old "dotcom" company headquartered in Atlanta is shown at the bottom of the page. An employee is to be
A team of consultants studied the service operation at the Wendy's Restaurant in the Woodbridge Mall in Woodbridge, New Jersey. They measured the time between customer arrivals to the restaurant over
In a study of tax write-offs by the affluent, Peter Dreier of Occidental College (Los Angeles) compiled the relative frequency distribution shown on the right.The distribution describes the incomes
Many real-world systems (e.g., electric power transmission, transportation, telecommunications, and manufacturing systems) can be regarded as capacitated-flow networks, whose arcs have independent
If x is a binomial random variable, compute p(x) for each of the following cases:a. n= S,x= 1,p= .2b. n=4,x=2,q= .4c. n =3,x= O,p= .7d. n=5,x=3,p=.1e. n = 4,x = 2,q = .6f. n= 3,x= 1,p= .9
If x is a binomial random variable, use Table I1 in Appendix B to find the following probabilities:a. P(X = 2) for n = 10, p = .4b. P(x I 5) for n = 15, p = .6c. P x > 1)for n = 5, p = .1d. Px i <
If x is a binomial random variable, calculate p, a', and a for each of the following:a. n = 25, p = .5b. n = 80, p = .2c. n = 100,p = .6d. n = 70,p = .9e. n = 60,p = .8f. n = 1,000,p = .04
Periodically, the Federal Trade Commission (FTC)monitors the pricing accuracy of electronic checkout scanners at stores to ensure consumers are charged the correct price at checkout. A 1998 study of
According to the Internal Revenue Service (IRS), the chances of your tax return being audited are about 15 in 1,000 if your income is less than $100,000 and 30 in 1.000 if your income is $100,000 or
As the baby boom generation ages, the number of employees injured on the job will continue to increase. A recent poll by the Gallup Organization sponsored by Philadelphia-based CIGNA Integrated Care
"Do you believe your children will have a higher standard of living than you have?"This question was asked of a national sample of American adults with children in a TirneKNN poll (Jan. 29, 1996).
According to Catalyst, a New York-based women's advocacy and research group, 12% of all corporate officers at the 500 largest U.S. corporations in 1999 were women, compared to 8% in 1995. (Atlanta
On January 28,1986, the space shuttle Challenger was totally enveloped in an explosive burn that destroyed the shuttle and resulted in the deaths of all seven astronauts aboard. A presidential
The number of bank mergers in the 1990s far exceeded any previous 10-year period in US. history. As mergers created larger and larger banks, many customers charged the mega-banks with becoming more
Assume that x is a random variable having a Poisson probability distribution with a mean of 1.5. Use Table I11 to find the following probabilities:a. P(x 5 3) h. P(x 2 3)c. P(x = 3)d. P(x = 0)c. P(x
Suppose x is a random variable for which a Poisson probability distribution with h = 5 provides a good characterization.a. Graphp(x) for x = 0, 1,2, ... ,IS.b. Find p and a for x, and locate p and
The Federal Deposit Insurance Corporation (FDIC), insures deposits of up to $100,000 in banks that are members of the Federal Reserve System against losses due to bank failure or theft. Over the last
As part of a project targeted at improving the services of a local bakery, a management consultant (L. Lei of Rutgers University) monitored customer arrivals for several Saturdays and Sundays. Using
The Environmental Protection Agency (EPA) issues pollution standards that vitally affect the safety of consumers and the operations of industry (The United States Government Manuul1998-1999). For
US. airlines fly approximately 48 billion passenger-miles per month and average about 2.63 fatalities per month(Statistical Abstract of the United States: 1998). Assume the probability distribution
University of New Mexico economists Kishore Gawande and Timothy Wheeler studied the effectiveness of the Maritime Safety Program of the US. Coast Guard by examining the records of 951 deep-draft
The number x of people who arrive at a cashier's counter in a bank during a specified period of time often exhibits (approximately) a Poisson probability distribution. If we know the mean arrival
In studying the product life cycle in the commercial mainframe computer market over the period 1968 to 1982, Shane Greenstein (Northwestern University) and James Wade (University of Illinois) found
Suppose x is a random variable best described by a uniform probability distribution with c = 20 and d = 45.Find the followmg probabilities:a. ~(20 5 x 5 30)b. ~(20 < x 5 30)c. P(X 2 30)d. ~(x 3 45)e.
Refer to Exercise 4.51. Find the value of a that makes each of the following probability statements true.a. P(X 2a) = .6b. P(X %a) = .25c. P(X Ia) = 1d. ~(4 5 x5a) = .5
The random variable x is best described by a uniform probability distribution with c = 100 and d = 200. Find the probability that x assumes a valuea. More than 2 standard deviations from p.b. Less
The random variable x is best described by a uniform probability distribution with mean 10 and standard deviation 1. Findc, d, and f(x). Graph the probability distribution.Applying the Concepts
The data set listed in the table was created using the MINITAB random number generator. Construct a relative frequency histogram for the data. Except for the expected variation in relative
During the recession of the late 1980s and early 1990s, many companies began tightening their reimbursement expense policies. For example, a survey of 550 companies by the Dartnell Corporation found
The reliability of a piece of equipment is frequently defined to be the probability,p, that the equipment performs its intended function successfully for a given period of time under specific
Find the following probabilities for the standard normal random variable z:a.~(-l
Find a value of the standard normal random variable z, call ~t zo, such thata. P(z 5 z,,) = ,2090b. P(z 5 zo) = .7090 C. P(-zo 5 z < zo) = .8472d. P(-z,, 5 z 5 z,,) = .I664e. P(z,, 5 z 5 0) = ,4798f.
The random variable x has a normal distribution with p = 1,000andcr = 10.a. Find the probability that x assumes a valuc more than 2 standard deviations from its mean. More than 3 standard deviations
Suppose x is a normally distributed random variable with p = 11 and a = 2. Find each of the following:a. ~(105 x 5 12)b. ~(6 5 x5 10)
Suppose x is a normally distributed random variable with p = 50 and a = 3. Find a value of the random variable, call it x,,, such thata. P(x 5 x,,) = 3413b. P(x > x,) = .025c. P(x > x,,) = .95d. P(41
The crop yield for a particular farm in a particular year is typically measured as the amount of the crop produced per acre. For example, cotton is measured in pounds per acre. It has bccn
The characteristics of an industrial filling process in which an expensive liquid is injected into a container was investigated in Journal of Quality Technology (July 1999). The quantity injected per
The problem of matching aircraft to passenger demand on each flight leg is called the flight assigvlment in the airline industry. Spill is defined as the number of passengers not carried because the
Government data indicate that the mean hourly wage for manufacturing workers in the United States is $14(Statistical Abstract of the United States: 1999). Suppose the distribution of manufacturing
In studying the dynamics of fish populations, knowing the length of a species at different ages is critical, especially for commercial fishermen. Fisheries Science (Feb.1995) published a study of the
Personnel tests are designed to test a job applicant's cognitive andlor physical abilities. An IQ test is an example of the former; a speed test involving the arrangement of pegs on a peg board is an
In baseball, a "no-hitter" is a regulation 9-inning game in which the pitcher yields no hits to the opposing batters. Chance (Summer 1994) reported on a study of nohitters in Major League Baseball
and standard deviation 1.10.a. What percentage of 9-inning MLB games result in fewer than 6 hits?b. Demonstrate, statistically, why a no-hitter is considered an extremely rare occurrence in MLB.
Before negotiating a long-term construction contract, building contractors must carefully estimate the total cost of completing the project. The process is complicated by the fact that total cost
A machine used to regulate the amount of dye dispensed for mixing shades of paint can be set so that it discharges an average of p milliliters (mL) of dye per can of paint.The amount of dye
Examine the sample data below.a. Construct a stem-and-leaf plot to assess whether the data are from an approximately normal distribution.b. Compute s for the sample data.c. Find the values of QL and
In Exercise 2.18(p. 45) you read about a Journal of Statistics Education study of team performance on games in which Mark McGwire (of the St. Louis Cardinals) and Sammy Sosa (of the Chicago Cubs) hit
The data on January 1999 sanitation scores for 121 cruise ships, first presented in Exercise 2.58(p. 74), are reproduced on page 225. Assess whether the sanitation scores are approximately normally
Refer to Exercise 2.36(p. 59) and the ages of the 50 most powerful women in corporate America as determined by Fortune (Oct. 25,1999). A MINITAB printout with summary statistics for the age
Refer to the New Jersey Chamber of Commerce1 Rutgers Business SchoolIArthur Andersen 1998 study of Generation Xers' expectations of their future careers, Exercise 2.59(p. 75). Recall that a total of
Assume that x is a binomial random variable with n and p as specified in parts a-f. For which cases would it be appropriate to use a normal distribution to approximate the bmomial distribution'?a. n
Assume that x is a binomiz 11 random variable wil n = 25 and p = .5. Use Table I1 of Appendix B and the normal approximation to find the exact and approximate values, respectively, for the following
Assume that x is a binomial random variable with n = 100 and p = .40. Use a normal approximation to find the following:Ia. P(X 5 35)Ib. ~(40 5 x 5 50)c. ~(x 2 38)Applying the Concepts
Refer to the FTC study of the pricing accuracy of supermarket electronic scanners, Exercise 4.30(p. 192).Recall that the probability that a scanned item is priced incorrectly is y3,, = .033. 1a.
The computer chips in today's notebook and laptop computers are produced from semiconductor wafers.Certain semiconductor wafers are exposed to an environment that generates up to 100 possible defects
In 1999, nearly 500,000 Americans underwent laser surgcry to correct their vision. While the majority of patients were pleased with the results, it is estimated that 1% of patients of corneal
In recent years, American consumers have come to regard credit cards as commodities. As a result, the credil card industry has become increasingly competitive. The table on p. 231 reports the
Refer to Exercise 4.35(p. 193). where the number of shuttle catastrophes caused by booster failure in n missions was treated as a binomial random variable. Using the binomial distribution and the
The Chronicle of Higher Education Almanac (Aug.27,1999) reports that the percentage of undergraduates in the United States receiving federal financial aid is 45% at public four-year institutions and
According to New Jersey Business (Feb. 1996), Newark International Airport's new terminal handles an average of 3,000 international passengers an hour, but is capable of handling twice that number.
The random variables x and y have exponential distributions with A = 3 and A = .75, respectively. Using Table V in Appendix B, carefully plot both distributions on the same set of axes.
Use Table V in Appendix B to determine the value of e-"'for each of the following cases.a. h=l,a=lb. A= 1,a=2.5c. A = 2.5, a = 3d. A = 5, a = .3
Suppose x has an exponential distribution with A = 3.Find the following probabilities:a. P(X > 2)b. P(X > 1.5)c. P(X > 3)d. ~(x > .45)
Suppose x has an exponential distribution with A = 2.5.Find the following probabilities:a. ~(x 5 3)b. P(X 5 4)c. P(X 5 1.6)d. ~(x 5 .4)
Suppose the random variable x has an exponential probability distribution with A = 2. Find the mean and standard deviation of x. Find the probability that x will assume a value within the interval f
University of Michigan researchers B. Wilkinson, N.Diedrich and E. Rothman, and C. Drummond of Indiana-Purdue University in Fort Wayne studied the duration between goals scored by the University of
Lack of port facilities or shallow water may require cargo on a large ship to be transferred to a pier using smaller craft. This process may require the smaller craft to cycle back and forth from
Product reliability has been defined as the probability that a product will perform its intended function satisfactorily for its intended life when operating under specified conditions. The
A part processed in a flexible manufacturing system(FMS) is routed through a set of operations, some of which are sequential and some of which are parallel. In addition, an FMS operation can be
The importance of modeling machine downtime correctly in simulation studies was discussed in Industrial Engineering (Aug. 1990).The paper presented simulation results for a single-machine-tool system
In an article published in the European Journal of Operutiontrl Research (Vol. 21, 1985) the vehicle-dispatching decisions of an airport-based taxi service were investigated. In modeling the system,
The probab~lity distribution shown here describes a population of measurements that can assume values of 0,2.4. and 6, each of which occur5 w~th the same relatlve frequency:a. List all the different
Simulate sampling from the population described in Exercise 4.105 by marking the values of x, one on each of four identical coins (or poker chips, etc.). Place the coins (marked 0,2,4, and 6) into a

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