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Business Statistics A Decision Making Approach 10th Edition David F. Groebner, Patrick W. Shannon, Phillip C. Fry - Solutions
A landscape contractor bids on jobs where he can make $3000 profit. The probabilities of getting 1, 2, 3, or 4 jobs per month are shown.Find the contractor€™s expected profit per month. Number of jobs 1 3 4 0.3 0.2 0.4 Probability 0.1
If a person rolls doubles when she tosses two dice, she wins $5. For the game to be fair, how much should she pay to play the game?
In Exercise 15, find the expectation if a person buys two tickets. Assume that the player’s ticket is replaced after each draw and that the same ticket can win more than one prize.In exercise 15A lottery offers one $1000 prize, one $500 prize, and five $100 prizes. One thousand tickets are sold
A 35-year-old woman purchases a $100,000 term life insurance policy for an annual payment of $360. Based on a period life table for the U.S. government, the probability that she will survive the year is 0.999057. Find the expected value of the policy for the insurance company.
When one die is rolled, the expected value of the number of dots is 3.5. In Exercise 20, the mean number of dots was found for rolling two dice. What is the mean number of dots if three dice are rolled?In exerciseConstruct a probability distribution for the sum shown on the faces when two dice are
Complete the following probability distribution if P(6) equals two-thirds of P(4). Then find μ, σ2, and σ for the distribution. 2 0.23 1 4 9. 6. P(X) ? 0.18 0.015
A bag contains five balls numbered 1, 2, 4, 7, and *. Choose two balls at random without replacement and add the numbers. If one ball has the *, double the amount on the other ball. Construct the probability distribution for this random variable X and calculate μ, σ2, and σ.
Compute the probability of X successes, using Table B in Appendix A.a. n = 15, p = 0.80, X = 12b. n = 17, p = 0.05, X = 0c. n = 20, p = 0.50, X = 10d. n = 16, p = 0.20, X = 3
Compute the probability of X successes, using the binomial formula.a. n = 6, X = 3, p = 0.03b. n = 4, X = 2, p = 0.18c. n = 5, X = 3, p = 0.63
Compute the probability of X successes, using the binomial formula.a. n = 9, X = 0, p = 0.42b. n = 10, X = 5, p = 0.37
A survey found that 10% of Americans believe that they have seen a UFO. For a sample of 10 people, find each probability:a. That at least 2 people believe that they have seen a UFOb. That 2 or 3 people believe that they have seen a UFOc. That exactly 1 person believes that he or she has seen a UFO
Twenty percent of Americans ages 25 to 74 have high blood pressure. If 16 randomly selected Americans ages 25 to 74 are selected, find each probability.a. None will have high blood pressure.b. One-half will have high blood pressure.c. Exactly 4 will have high blood pressure.
A student takes a 20-question, multiple-choice exam with five choices for each question and guesses on each question. Find the probability of guessing at least 15 out of 20 correctly. Would you consider this event likely or unlikely to occur? Explain your answer.
Three out of four people think most advertising seeks to persuade people to buy things they don’t need or can’t afford. Find the probability that exactly 5 out of 9 randomly selected people will agree with this statement.
In 2014 the percentage of the U.S. population that speak English only in the home is 78.9%. Choose 15 U.S. people at random. What is the probability that exactly one-third of them speak English only? At least one-third? What is the probability that at least 9 do not speak English in the home?
Forty percent of prison inmates were unemployed when they entered prison. If 5 inmates are randomly selected, find these probabilities:a. Exactly 3 were unemployed.b. At most 4 were unemployed.c. At least 3 were unemployed.d. Fewer than 2 were unemployed.
Twenty-five percent of commercial airline accidents are caused by bad weather. If 300 commercial accidents are randomly selected, find the mean, variance, and standard deviation of the number of accidents caused by bad weather.
Find the mean, variance, and standard deviation for the number of heads when 10 coins are tossed.
In 2014 the percentage of the U.S. population who was foreign-born was 13.1. Choose 60 U.S. residents at random. How many would you expect to be American-born? Find the mean, variance, and standard deviation for the number who are foreign-born.
It has been reported that 83% of federal government employees use e-mail. If a sample of 200 federal government employees is selected, find the mean, variance, and standard deviation of the number who use e-mail.
A survey found that 21% of Americans watch fireworks on television on July 4. Find the mean, variance, and standard deviation of the number of individuals who watch fireworks on television on July 4 if a random sample of 1000 Americans is selected.
Eighty-five percent of Americans favor spending government money to develop alternative sources of fuel for automobiles. For a random sample of 120 Americans, find the mean, variance, and standard deviation for the number who favor government spending for alternative fuels.
A survey found that 25% of pet owners had their pets bathed professionally rather than do it themselves. If 18 pet owners are randomly selected, find the probability that exactly 5 people have their pets bathed professionally.
In a survey, 63% of Americans said they own an answering machine. If 14 Americans are selected at random, find the probability that exactly 9 own an answering machine.
Thirty-two percent of adult Internet users have purchased products or services online. For a random sample of 200 adult Internet users, find the mean, variance, and standard deviation for the number who have purchased goods or services online.
Fifty-eight percent of runaways in the United Stated are female. In 20 runaways are selected at random, find the probability that exactly 14 are female.
In a recent year, 13% of businesses have eliminated jobs. If 5 businesses are selected at random, find the probability that at least 3 have eliminated jobs during that year.
Of graduating high school seniors, 14% said that their generation will be remembered for their social concerns. If 7 graduating seniors are selected at random, find the probability that either 2 or 3 will agree with that statement.
Is this a binomial distribution? Explain. 2 0.432 1 0.288 3 0.216 P(X) 0.064
Show that the mean for a binomial random variable X with n = 3 is 3p.
The probabilities are 0.50, 0.40, and 0.10 that a trailer truck will have no violations, 1 violation, or 2 or more violations when it is given a safety inspection by state police. If 5 trailer trucks are inspected, find the probability that 3 will have no violations, 1 will have 1 violation, and 1
The probability that a person has 1, 2, 3, or 4 prescriptions when he or she enters a pharmacy is 0.5, 0.3, 0.15, or 0.05. For a sample of 10 people who enter the pharmacy, find the probability that 3 will have one prescription filled, 3 will have two prescriptions filled, 2 will have three
Find each probability P(X; λ), using Table C in Appendix A.a. P(6;4)b. P(2;5)c. P(7;3)
Find each probability P(X; λ) using Table C in Appendix A.a. P(10; 7)b. P(9; 8)c. P(3; 4)
In a 400-page manuscript, there are 200 randomly distributed misprints. If a page is selected, find the probability that it has 1 misprint.
A nursery provides red impatiens for commercial landscaping. If 5% are variegated instead of pure red, find the probability that in an order for 200 plants, exactly 14 are variegated.
Of a company’s mailings 1.5% are returned because of incorrect or incomplete addresses. In a mailing of 200 pieces, find the probability that none will be returned.
If 3% of all cars fail the emissions inspection, find the probability that in a sample of 90 cars, 3 will fail. Use the Poisson approximation.
The average number of phone inquiries per day at the poison control center is 4. Find the probability it will receive 5 calls on a given day. Use the Poisson approximation.
In a batch of 2000 calculators, there are, on average, 8 defective ones. If a random sample of 150 is selected, find the probability of 5 defective ones.
A school newspaper staff is comprised of 5 seniors, 4 juniors, 5 sophomores, and 7 freshmen. If 4 staff members are chosen at random for a publicity photo, what is the probability that there will be 1 student from each class?
Twelve people apply for a teaching position in mathematics at a local college. Six have a PhD and six have a master’s degree. If the department chairperson selects three applicants at random for an interview, find the probability that all three have a PhD.
Ten people apply for a job at Computer Warehouse. Five are college graduates and five are not. If the manager selects 3 applicants at random, find the probability that all 3 are college graduates.
A person calls people to ask if they would like to extend their automobile insurance beyond the normal 3 years. The probability that the respondent says yes is about 33%. If she calls 12 people, find the probability that the first person to say yes will occur with the fourth customer.
A soda pop manufacturer runs a contest and places a winning bottle cap on every sixth bottle. If a person buys the soda pop, find the probability that the person will(a) Win on his first purchase,(b) Win on his third purchase,(c) Not win on any of his first five purchases.
Mark shoots arrows at a target and hits the bull’s-eye about 40% of the time. Find the probability that he hits the bull’s-eye on the third shot.
At an amusement park basketball game, the player gets 3 throws for $1. If the player makes a basket, the player wins a prize. Mary makes about 80% of her shots. Find the probability that Mary wins a prize on her third shot.
A card is randomly drawn from a deck of cards and then replaced. The process continues until 3 clubs are obtained. Find the average number of trials needed to get 3 clubs.Another type of problem that can be solved uses what is called the negative binomial distribution, which is a generalization of
An 8-sided die is rolled. The sides are numbered 1 through 8. Find the average number of rolls it takes to get two 5s.Another type of problem that can be solved uses what is called the negative binomial distribution, which is a generalization of the binomial distribution. In this case, it tells the
Cards are drawn at random from a deck and replaced after each draw. Find the average number of cards that would be drawn to get 4 face cards.Another type of problem that can be solved uses what is called the negative binomial distribution, which is a generalization of the binomial distribution. In
About 4% of the citizens of the United States have type AB blood. If an agency needed type AB blood and donors came in at random, find the average number of donors that would be needed to get a person with type AB blood.Another type of problem that can be solved uses what is called the negative
It is estimated that 4 out of 5 men prefer showers to baths. Find the mean and standard deviation for the distribution of men who prefer showers to baths.The mean of a geometric distribution is μ = 1/p, and the standard deviation is σ = √q/p2, where p = the probability of the outcome and q = 1
About 2 out of every 3 children take some kind of lessons outside of school. These lessons include music, art, and sports. Find the mean and standard deviation of the distribution of the number of children who take lessons outside of school.The mean of a geometric distribution is μ = 1/p, and the
One in five teachers stated that he or she became a teacher because of the long summer vacations. Find the mean and standard deviation for the distribution of teachers who say they became teachers because of the long summer vacation.The mean of a geometric distribution is μ = 1/p, and the standard
One worker in four in America admits that she or he has to do some things at work that go against her or his consciences. Find the mean and standard deviation for the distribution of workers who admit to having to do some things at work that go against their consciences.The mean of a geometric
Determine whether the distribution represents a probability distribution. If it does not, state why. 15 10 0.1 10 х 0.3 0.4 P(X)
Determine whether the distribution represents a probability distribution. If it does not, state why. P(X) 10 10 10 |-12 2.
Determine whether the distribution represents a probability distribution. If it does not, state why. 16 9. 4 9. |х 1 P(X)
At Shoe World, the manager finds the probability that a woman will buy 1, 2, 3, or 4 pairs of shoes is shown. Construct a graph for the distribution. Number X 1 3 0.08 4 0.02 Probability P(X) 0.63 0.27
A bank has a drive-through service. The number of customers arriving during a 15-minute period is distributed as shown. Find the mean, variance, and standard deviation for the distribution. Number of customers X Probability P(X) 3 4 0.25 0.12 0.20 0.31 0.12
A phone service center keeps track of the number of customers it services for a random 1-hour period during the day. The distribution is shown.Find the mean, variance, and standard deviation for the data. Based on the results of the data, how many service representatives should the store employ?
A producer plans an outdoor regatta for May 3. The cost of the regatta is $8000. This includes advertising, security, printing tickets, entertainment, etc. The producer plans to make $15,000 profit if all goes well. However, if it rains, the regatta will have to be canceled. According to the
In a retirement community, 14% of cell phone users use their cell phones to access the Internet. In a random sample of 10 cell phone users, what is the probability that exactly 2 have used their phones to access the Internet? More than 2?
Fifty-eight percent of people surveyed said that they would take a ride in a fully self-driving automobile. Find the mean, variance, and standard deviation of the number of people who would agree to ride in the self-driving automobile if 250 people were asked.
American Energy Review reported that 27% of American households burn wood. If a random sample of 500 American households is selected, find the mean, variance, and standard deviation of the number of households that burn wood.
Three out of four American adults under age 35 have eaten pizza for breakfast. If a random sample of 20 adults under age 35 is selected, find the probability that exactly 16 have eaten pizza for breakfast.
According to survey records, 75.4% of women aged 20–24 have never been married. In a random sample of 250 young women aged 20–24, find the mean, variance, and standard deviation for the number who are or who have been married.
After a recent national election, voters were asked how confident they were that votes in their state would be counted accurately. The results are shown below.46% Very confident...........41% Somewhat confident9% Not very confident.......4% Not at all confidentIf 10 voters are selected at random,
Before a DVD leaves the factory, it is given a quality control check. The probabilities that a DVD contains 0, 1, or 2 defects are 0.90, 0.06, and 0.04, respectively. In a sample of 12 DVDs, find the probability that 8 have 0 defects, 3 have 1 defect, and 1 has 2 defects.
The probability that an accounting company will make 0, 1, 2, or 3 errors in preparing a yearly budget for a small company is 0.50, 0.28, 0.15, and 0.07 respectively. If 20 companies have the firm prepare their budgets, find the probability that 9 will contain 0 errors, 6 will contain one error, 3
Transportation officials reported that 8.25 out of every 1000 airline passengers lost luggage during their travels last year. If we randomly select 400 airline passengers, what is the probability that 5 lost some luggage?
The number of boating accidents on Lake Emilie follows a Poisson distribution. The probability of an accident is 0.003. If there are 1000 boats on the lake during a summer month, find the probability that there will be 6 accidents.
If 5 cards are drawn from a deck, find the probability that 2 will be hearts.
Of the 50 automobiles in a used-car lot, 10 are white. If 5 automobiles are selected to be sold at an auction, find the probability that exactly 2 will be white.
At a food bank a case of donated items contains 10 cans of soup, 8 cans of vegetables, and 8 cans of fruit. If 3 cans are selected at random to distribute, find the probability of getting 1 can of vegetables and 2 cans of fruit.
A die is rolled until a 3 is obtained. Find the probability that the first 3 will be obtained on the fourth roll.
A card is selected at random from an ordinary deck and replaced. Find the probability that the first face card will be selected on the fourth draw.
Cyber Communications, Inc., has a new cell phone product under development in the research and development (R&D) lab. It will increase the megapixel capability of cell phone cameras to the 12+ range. The head of R&D made a presentation to the company CEO stating that the probability the
In a large metropolitan area, 65% of commuters ride the train only, 18% ride the bus only, and 6% ride both the train and the bus to get to the central business district.a. What is the probability that a randomly selected commuter does not ride the train to the central business district?b. What is
In a large shipment of electronic parts, 0.015 are bad. The parts are tested using a machine that correctly identifies bad parts as defective with a probability of 0.98, and correctly identifies good parts as non defective with a probability of 0.95.a. If a part is randomly sampled from the
A large coffeehouse has found that 50% of all customers order food, 80% order coffee, and 40% order both. What is the probability that a customer at the coffeehousea. Orders food but no coffee?b. Orders coffee but no food?c. Orders neither coffee nor food?
After spending some time studying company e-mail accounts, the manager of computer security for a large insurance company has determined that 25% of all e-mail messages sent to employee computers are spam. If 80% of all spam e-mails sent to personal accounts contain the word guarantee in the
Based on a survey conducted by students in the Recreational Management degree program, 65% of students at the university own a mountain bike, 25% own a road bike, and 6% own both a mountain bike and a road bike.a. What is the probability that a randomly selected student at this university has a
Thirty-five percent of all customers of a large, national financial institution manage their accounts online. What is the probability that in a random sample of three customers from the financial institution’s database,a. All three manage their accounts online?b. Exactly two manage their accounts
Five hundred smartphone owners were asked if they use their phones to download sports scores. The responses are summarized in the following table:a. What is the probability that a randomly sampled respondent from this group has used his or her smartphone to download sports scores?b. What is the
An April 14, 2015, article by Kara Brandeisky on Money magazine’s website states that overall the chance of being audited by the IRS in 2014 was 0.86%. If a person’s adjusted gross income was between $50,000 and $74,999, the chance of being audited drops to 0.53%, and for those with incomes
When customers call into a bank’s customer service phone line, they are asked to complete a survey on service quality at the end of the call. Six out of ten customers agree to do the survey. Of those who agree, 58% actually respond to all the questions.a. Calculate the probability that a randomly
The loan manager for High Desert Bank selected a sample of the loans her bank has made in the past year. The file High Desert Banking contains information on the loan amount, the type of loan, and the region of the state where the loan was made.a. What is the probability of randomly selecting a
ECCO is a company that makes backup alarms for commercial vehicles and heavy-duty equipment like forklifts. The data file ECCO contains warranty claim data as well as the associated manufacturing plant, complaint code, and shift for each alarm that is manufactured.a. Based on the data provided,
Trucks that travel on U.S. highways have to stop at various locations to be weighed and inspected for safe brakes and light systems. Of these trucks, 77% are on interstate commerce business while 23% are intrastate. Of the intrastate trucks, 3.1% are flagged for safety defects compared to 0.7% of
A Bipartisan Policy Center article indicated that 57.5% of the voting-age voters cast ballots in the 2012 presidential election. It also indicated that 70% of registered voters voted in the election. The percent of those who voted for President Obama was 51.01%.a. Determine the proportion of
Online marketplaces such as Craigslist have become a popular way for individuals to buy and sell miscellaneous items. The table below shows the numbers of days products stayed active (not sold) on one of these sites and also the price range of the items.a. Using the relative frequency approach to
A hair salon caters to both men and women. In addition to hairstyles, the salon provides back and shoulder massages. In the past, 42% of men have requested a massage and 61% of women have requested a massage. The salon’s customers are 48.2% men and 51.8% women.a. If a customer arrives for a hair
Based on a USA Today online article by Kevin McCoy (“IRS audit rate for individuals drops,” www.usatoday.com, Feb. 24, 2015), an individual taxpayer’s chance of being audited in 2014 was 0.0086, the lowest in ten years.a. Discuss the type of probability assessment used to arrive at the 0.0086
A survey of 490 workers included the question €œIn your opinion, is it OK for a company to monitor its employees€™ Internet use?€ The possible responses were:(1) Only after informing the employees,(2) Does not need to inform the employees,(3) Only when company
Use a tree diagram to list the sample space for the number of movies rented by three customers at a Red Box video kiosk where customers are allowed to rent one, two, or three movies (assuming that each customer rents at least one movie).
A manufacturing company operates three shifts daily. Each shift produces two models: A and B. A random sample of daily production has been taken, and the results are in the file Shift Production.a. Develop a box and whisker plot that compares daily production by shift and model.b. Is there a
A coffee shop would like to compare the dollar purchases of customers who use the drive-thru and those who come inside. A random sample of inside and drivethru purchases is taken, and the results are contained in the file Coffee Shop Sales.a. Develop a box and whisker plot to compare the dollar
The AJ Fitness Club is a full-service fitness center that offers its members the latest in weight machines, cardio equipment, and exercise classes. The company has surveyed its members to learn how satisfied they are with the services provided by the club. The data for this survey are in the file
A company in Silicon Valley periodically offers its employees a full health screen in which data are collected on several characteristics including percent body fat. Data for a sample of employees are in the file Bodyfat. Use percent body fat as the variable of interest in the following
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