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mathematics
introduction to business statistics
Introduction To Business Statistics 6th Edition Ronald M. Weiers - Solutions
For the normal distribution described in Exercise 7.11, what is the probability that a randomly selected first mortgage would have been for an amounta. Between $239,000 and $259,000?b. Over $259,000? c. Under $324,000?
For the normal distribution described in Exercise 7.10, what is the probability that a randomly selected passenger trip would have produced a revenuea. Between $1.05 and $1.30?b. Over $1.40? c. Under $0.75?
Using the standard normal table, determine a z value (to the nearest two decimal places) such that the areaa. From the midpoint to z is 0.20.b. From the midpoint to z is 0.48.c. Between z and negative infinity is 0.54.d. Between z and positive infinity is 0.30.
Using the standard normal table, determine a z value (to the nearest two decimal places) such that the areaa. From the midpoint to z is 0.2486.b. From the midpoint to z is 0.3554.c. Between z and negative infinity is 0.0694.d. Between z and positive infinity is 0.0212.
The normal distribution is really a family of distributions. Is the standard normal distribution also a family of distributions? Explain.
A study by the National Golf Foundation reports that the 6.2 million golfers over the age of 50 spent an average of $939 on golf during the previous year. Assuming a normal distribution with a standard deviation of $200, what is the probability that a randomly selected golfer in this age group will
It has been reported that the average hotel check-in time, from curbside to delivery of bags into the room, is 12.1 minutes. An Li has just left the cab that brought her to her hotel. Assuming a normal distribution with a standard deviation of 2.0 minutes, what is the probability that the time
In 1999, the average charge for tax preparation by H&R Block, Inc. was $84.57. Assuming a normal distribution and a standard deviation of σ = $10, what proportion of H&R Block’s tax preparation fees were a. More than $84.57?b. Between $64.57 and $104.57?c. Between $74.57 and
In 2004, the average conventional first mortgage for new single-family homes was $294,000. Assuming a normal distribution and a standard deviation of σ = $30,000, what proportion of the mortgages werea. More than $294,000?b. Between $234,000 and $354,000?c. Between $264,000 and $324,000?d. More
The Canada Urban Transit Association has reported that the average revenue per passenger trip during a given year was $1.05. If we assume a normal distribution and a standard deviation of σ = $0. 20, what proportion of passenger trips produced a revenue ofa. Less than $1.05?b. Between $0.65 and
Sketch two different normal distributions along a single x axis so that both of the following conditions are satisfied: (a) µa = µb and b σ a > σ b.
In the normal distribution, the probability that x will exceed (µ + 2σ) is the same as the probability that x will be less than (µ - 2σ). What characteristic of the normal distribution does this reflect?
It has been stated that the normal distribution is really a “family” of distributions. Explain.
What is the probability that a continuous random variable will take on any specific value? Explain your answer.
J. D. Power and Associates’ Initial Quality Study reports that the industry-average problem rate for vehicles is 154 problems per 100 vehicles. The highest-rated marque was Acura, with a rate of just 91 problems per 100 vehicles. On the other hand, Kia was reported as having 251 problems per 100
According to the National Insurance Crime Bureau, the metropolitan area with the highest incidence of auto theft is Miami, Florida, with an annual rate of 2.6 thefts for every 100 vehicles registered in 1997. a.The University of Miami has approximately 1100 faculty members. b Under the
It has been estimated that about 30% of families with an annual income of $100,000 or more own savings bonds. What is the probability that exactly three of a randomly selected group of five such families own savings bonds?
It has been estimated that 40% of all U.S. children are covered by life insurance. For a randomly selected group of 10 children, use the appropriate statistical table to describe the probability distribution for x = the number in the sample who are covered by life insurance.
During the 1999 tax filing season, 13.7% of all individual U.S. tax returns were prepared by H&R Block. For a random selection of 3 tax returns, describe the probability distribution for x = the number in the sample whose returns were prepared by H&R Block.
During 2001, the crash rate for commuter air carriers was 2.1 per 100,000 flying hours. Assuming this rate continues, what is the probability that there will be no more than one crash in the next 50,000 flying hours?
The U.S. Department of Transportation reports that America West Airlines got 7.65 complaints of mishandled baggage per 1000 passengers in March 2000. Assuming this rate applies to the next 500 passengers who depart from Portland, Oregon, on America West flights, what is the probability that at
According to the Mortgage Bankers Association of America, the foreclosure rate on home mortgages in 2001 was 1%. Assuming that this rate is applicable to a community where 1000 homes have mortgages, use the Poisson approximation to the binomial distribution to determine the following for x = the
The U.S. divorce rate has been reported as 3.8 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed, and that x = the number of divorces in this community during the coming year, determine the following:a. E(x)b. P(x = 1)c.
In 2000, there were about 530 motor vehicle thefts for every 100,000 registrations. Assuming (1) A Poisson distribution, (2) A community with a comparable theft rate and 1000 registered motor vehicles, and (3) x = the number of vehicles stolen during the year in that community,
Airlines book more seats than are actually available, then “bump” would-be passengers whenever more people show up than there are seats. In 2001, the rate at which passengers were bumped was 1.87 per 1000 passengers. Assuming that, on average, the probability of any given passenger being bumped
Seven trials are conducted in a Bernoulli process in which the probability of success in a given trial is 0.7. If x = the number of successes, determine the following:a. E(x)b. σc. P(x = 3)d. P(3 ≤ x ≤ 5)e. P(x >4)
When we are sampling without replacement, under what conditions can we assume that the constant π assumption has been satisfactorily met?
In 2004, nearly 24 million tons of steel mill products went to construction and contracting companies. Transco Steel, a hypothetical manufacturer specializing in the production of steel for this market, is faced with aging production facilities and is considering the possible renovation of its
A contractor must pay a $40,000 penalty if construction of an expensive home requires more than 16 weeks. He will receive a bonus of $10,000 if the home is completed within 8 weeks. Based on experience with this type of project, the contractor feels there is a 0.2 chance the home will req uire more
Scam artists sometimes “stage” accidents by purposely walking in front of slow-moving luxury cars whose drivers are presumed to carry large amounts of liability insurance. The “victim” then offers to accept a small monetary cash settlement so the driver can avoid an insurance claim, a blot
Ed Tompkins, the assistant dean of a business school, has applied for the position of dean of the school of business at a much larger university. The salary at the new university has been advertised as $120,000, and Ed is very excited about this possibility for making a big career move. He has been
The values of x in a discrete probability distribution must be both exhaustive and mutually exclusive. What is meant by these two terms?
Why is a random variable said to be “random”?
The president of a computer manufacturing firm states that there is a 70% chance that industry shipments of notebook computers will double in the next 5 years. Is this a classical probability, a relative frequency probability, or a subjective probability?
If A = “Aeroflot, Russia’s national airline, will begin making daily flights to Pocatello, Idaho, next year,” identify the sample space and possible events that could occur. Use your judgment in arriving at an approximate probability for the event(s) and complement(s) you’ve
If B = “IBM’s net profit will increase next year,” identify the sample space and possible events that could occur. Use your judgment in arriving at an approximate probability for the event(s) and complement(s) you’ve identified.
Electric meters on private homes in a community register the cumulative consumption of kilowatt-hours with a five-digit reading. If a home in the community were randomly selected, it’s possible that the right-hand digit (which spins the fastest) would be a “7.” Using the concept of classical
Regarding Exercise 5.4, how might an observer employ the law of large numbers to verify the classical probability that you identified?In ExerciseElectric meters on private homes in a community register the cumulative consumption of kilowatt-hours with a five-digit reading. If a home in the
If a die is rolled one time, classical probability would indicate that the probability of a “two” should be . If the die is rolled 60 times and comes up “two” only 9 times, does this suggest that the die is “loaded”? Why or why not?
A newspaper article reported that Massachusetts had become the second state (after Montana) to prohibit sex to be used as a factor in determining insurance premiums. Considering the information in Table 5.1, would such unisex insurance tend to increase or decrease the life insurance premiums
It has been reported that about 35% of U.S. adults attended a sports event during the previous year. What are the odds that a randomly selected U.S. adult attended a sports event during the year?
If the odds are 4:7 that an event will occur, what is the corresponding probability?
The following contingency table of frequencies is based on a 5-year study of fire fatalities in Maryland. For purposes of clarity, columns and rows are identified by the letters A€“C and D€“G, respectively.a. For this table, identify any two events that are mutually exclusive.b.
Using the table in Exercise 5.12, what is the probability that a randomly selected victim would have been at least 60 years old and have had a blood alcohol level of at least 0.10%?
A survey of employees at a large company found the following relative frequencies for the one-way distances they had to travel to arrive at work:a. What is the probability that a randomly selected individual will have to travel 11 or more miles to work?b. What is the probability that a randomly
In 2005, McDonald’s had 31,886 restaurants systemwide. Of these, 18,334 were operated by franchisees, 9283 by the company, and 4269 by affiliates. What is the probability that a randomly selected McDonald’s restaurant is operated by either a franchisee or an affiliate?
It has been reported that the 44,300 employees of Northwest Airlines are distributed among the following corporate functions:For the sample space consisting of Northwest employees:a. Draw a Venn diagram representing events A, B, C, D, and E.b. What is the value of P(A)?c. What is the value of P(A
In 2003, Entergy Corporation had 2,631,752 electricity customers. Of these, 86.0% were in the residential category (R); 11.8% were commercial (C); 1.6% were industrial (I); and 0.6% were government and municipal (G).a. Draw a Venn diagram representing events R, C, I, and G.b. What is the value of
Using the information presented in the table in Exercise 5.15, calculate the following probabilities:a. P(D or N) b. P(D′ or N′)c. P(D or N′) d. P(D′ or N)
What is the difference between a marginal probability and a joint probability?
A study by the U.S. Energy Information Administration found that 84.3% of U.S. households with incomes under $10,000 did not own a dishwasher while only 21.8% of those in the over-$50,000 income range did not own a P(AB) dishwasher. If one household is randomly selected from each income
Through April 30 of the 1999 filing season, 13.7% of all individual U.S. tax returns were prepared by H&R Block.a. If two individuals are randomly selected from those filing tax returns during this period, what is the probability that both of their tax returns were prepared by H&R Block?b.
Of employed U.S. adults age 25 or older, 90.3% have completed high school, while 30.8% have completed college. For H completed high school, C completed college, and assuming that one must complete high school before completing college, construct a tree diagram to assist your calculation of the
A magician has two coins: one is unbalanced and lands heads 60% of the time; the other is fair and lands heads 50% of the time. A member of the audience randomly selects one of the coins and flips it. The result is heads.a. What is the prior probability that the fair coin was selected?b. Given
A tax accountant has three choices for the method of treating one of a client’s deductions. After this choice has been made, there are only two choices for how a second deduction can be treated. What is the total number of possibilities for the treatment of the two deductions?
A committee consists of eight members, each of whom may or may not show up for the next meeting. Assuming that the members will be making independent decisions on whether or not to attend, how many different possibilities exist for the composition of the meeting?
Ten prominent citizens have been nominated for a community’s “Citizen of the Year” award. First- and second-place trophies are awarded to the two persons receiving the highest and second-highest number of votes. In how many different ways can the trophies be awarded?
In advertising her oceanfront cottage for summer rental, a property owner can specify (1) Whether or not pets are permitted, (2) Whether the rent will be $700, $900, or $1200 per week, (3) Whether or not children under 10 are allowed, and (4) Whether the maximum stay is 1, 2, or
A state’s license plate has 6 positions, each of which has 37 possibilities (letter, integer, or blank). If the purchaser of a vanity plate wants his first three positions to be ROY, in how many ways can his request be satisfied?
When we are considering n objects taken r at a time, with r > 1, why will the number of combinations be less than the number of permutations?
When we are considering n objects taken r at a time, with r > 1, why will the number of combinations be less than the number of permutations?
Collecting data on traffic accident fatalities, the National Highway Traffic Safety Administration has found that 47.1% of the victims have 0.0% blood alcohol content (BAC), 7.0% of the victims have from 0.01 to 0.07% BAC, and 45.9% of the victims have at least 0.08% BAC. For a randomly selected
Data from the Federal Bureau of Investigation show that 1 of every 189 motor vehicles was stolen during 2000. Applying this statistic to 5 motor vehicles randomly selected from the nation’s vehicle population:a. What is the probability that none of the 5 motor vehicles will be stolen?b. What is
In 2001, the average U.S. production employee worked 34.2 hours per week. An assistant in the human resources department of Acme Eyebolts, Inc., is curious as to how the workers in her company compared to this figure during the first week of this month. The assistant will be reaching her
college of business has 20 faculty members in Accounting, 30 in Marketing, 20 in Management, 15 in Finance, and 15 in Information Systems. The dean of the college asks her secretary to arbitrarily select 4, 6, 4, 3, and 3 persons from the respective departments to serve on a faculty committee. Is
Of a company’s 1000 employees, 200 are managers, 700 are factory employees, and 100 are clerical. In selecting a sample of 100 employees, a researcher starts at the beginning of the alphabet and continues until she has collected the names of 20 managers, 70 factory employees, and 10 clerical
To test the effectiveness of a new type of plastic handcuffs, a law enforcement agency puts the cuffs on a sample of 30 persons who belong to the local weightlifting club. None is able to break free from the cuffs. What type of sampling technique does this represent? Explainyour reasoning.
A researcher wants to find out to what extent local residents participate in the recreation and entertainment activities available in their community. She selects a simple random sample of numbers from the telephone directory and proceeds to call these numbers between 6 P.M. and 9 P.M. If the line
One of the capabilities on the Internet is called “reverse lookup.” Enter the residential telephone number for someone you know. Evaluate the accuracy of the name and address provided, along with the validity of the map that can be generated as additional information. Was the reverse lookup
A study found that the average American buys 4.6 movie tickets per year, compared to just 1.9 for the average Spaniard. Assuming that the data values in file XR04049 represent the number of movie ticket purchases reported by 100 American respondents,a. Select a simple random sample of 20 data
To obtain a sample of the invoices over the past year, a clerk uses the computer to select all invoice numbers that are a multiple of 13. If the invoice numbers are sequential, beginning with 1, what type of sample does this represent?
Attendees at an industrial trade show are given the opportunity to fill out a card that entitles them to receive a free software package from the sponsoring firm. The cards are placed in a bin, and 30 winners will be drawn. Considering the 30 winners as a sample from all of the persons filling out
In survey research, what are some of the methods by which we can reduce nonsampling error?
To impress the interviewer, many respondents in a survey of 400 persons exaggerated their annual incomes by anywhere from 2% to 50%. Does such exaggeration represent sampling error or nonsampling error? Explain.
Differentiate between the terms parameter and statistic. Which one will be the result of taking a sample?
Provide a real or hypothetical example of a situation in which the sampling process is destructive.
What is the difference between a sample and a census? Why can it be advantageous to select a sample instead of carrying out a census?
Using one or more search engines and key words of your choice, find (a) A website that reports the average life span of Saint Bernard dogs and (b) A website that advises business professionals on strategies for writing an effective memo.
Using your browser’s “people finder” capability, find out how many telephone listings are in your state for people with the same last name as yours. How many listings are there in your state for people named Smith?
Besides accounting and financial information, what are some of the other sources of internal secondary data?
When traveling, some motorists assume that a restaurant has good food and reasonable prices if there are a lot of trucks parked outside. What other observed characteristics of a restaurant might a traveler use in deciding whether to stop and eat?
In a health study, the dietary habits of 420,000 men were examined over a 3-year period. For those who ate no fried foods, the death rate was 1208 per 100,000 man-years. For men who consumed fried foods more than 15 times a week, the corresponding rate was only 702. Considering that the
A direct-mail firm tries two different versions of a mailing, one of which includes a 50-cent monetary incentive for the respondent. Responses to the mailing with the incentive were 15% higher than for a similar mailing without it. a. Identify the dependent and independent variables in this
In studying the effectiveness of monetary rewards on seat belt usage, a firm has been giving out lottery tickets to employees wearing their belts when entering the company parking area. At the end of each week, the holder of the winning ticket gets a free dinner at a local restaurant. Before the
A company has constructed two prototypes of a new personal digital assistant (PDA) and would like to find out which one of the two looks easier to use. Of the three types of surveys discussed in this section, which one would the company not wish to employ?
A research firm finds that only 33% of those who reported buying Kellogg’s Frosted Flakes had actually purchased the product during the period monitored. What type of survey research error does this represent?
Comment on the appropriateness of the question, “Have you ever broken the law and endangered the lives of others by running a red light?”
What are the major approaches to carrying out survey research?
A published article reports that 60% of U.S. households have cable television. The president of an electronics firm clips the item from the paper and files it under “Cable TV data.” Would this material be considered primary data or secondary data?
Based on your results and responses to the previous questions, does the screening test appear to be potentially useful as one of the factors in helping Baldwin predict whether a given applicant will end up defaulting on his or her computer loan?
Construct adjacent dotplots (use box plots if the dotplot feature is not available on your computer statistical package) and visually compare the screening test scores of students who did not default on their computer loan to the scores of those who defaulted. Does the distribution of screening
In the descriptive statistics of the screening test scores for the students who did not default, identify the value of the third quartile and interpret its meaning. If this numerical value had been established as a cutoff for receiving a computer loan, what percentage of those who repaid would have
Generate appropriate descriptive statistics of the screening test scores for those who did not default on their computer loan. Be sure to include the mean and the third quartile. Do the same for those who did default, then compare the results. Is the mean score on the screening test higher for
During 1999, 1,220,130 college-bound high school seniors took the Scholastic Aptitude Test (SAT). The average score on the mathematics component was 511, with a standard deviation of 114.We are assuming that the SATmath scores in data file XR03067 could have been the math scores for a sample of 400
Bride’s magazine reports the cost of the average honeymoon as $3657. Assume that their findings could have been based on the honeymoon expenditures of a sample consisting of 300 couples whose costs are listed in data file XR03066.a. Confirm the mean and determine the median and the standard
According to the Energy Information Administration, the average U.S. household spends $1338 per year for utilities (including heat, electricity, cooling, and water). The averages by region were as follows: Northeast ($1644), Midwest ($1396), South ($1328), and West ($1014). Assume that the findings
A law enforcement agency, administering breathalyzer tests to a sample of drivers stopped at a New Year€™s Eve roadblock, measured the following blood alcohol levels for the 25 drivers who were stopped:a. Calculate the mean and standard deviation for this sample.b. Use
For a sample of 5 different years from the period 1960 through 1998, it is found that U.S. work stoppages involving at least 1000 workers occurred 268 times in one of these years, with 424, 235, 145, and 44 work stoppages in the other four.a. Determine the mean, median, range, and midrange.b.
The frequency distribution for population density (persons per square mile) for the 50 U.S. states is as follows:Population Density Number of States0–under 100............................................................ 27100–under
During fiscal year 1986, McDonnell Douglas Corporation was second only to Lockheed Missiles & Space Company in net value of U.S. Department of Defense prime contract awards over $25,000 for research, development, test, and evaluation. The work awarded to McDonnell Douglas was done in 20
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