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mathematics
statistics
Statistics For Management And Economics Abbreviated 10th Edition Gerald Keller - Solutions
After watching a number of children playing games at a video arcade, a statistics practitioner estimated the following probability distribution of X, the number of games per visit.a. What is the probability that a child will play more than four games?b. What is the probability that a child will
Refer to Exercise 7.23. Suppose that each game costs the player 25 cents. Use the laws of expected value and variance to determine the expected value and variance of the amount of money the arcade takes in.
A survey of Amazon.com shoppers reveals the following probability distribution of the number of books purchased per hit.a. What is the probability that an Amazon.com visitor will buy four books?b. What is the probability that an Amazon.com visitor will buy eight books?c. What is the probability
A university librarian produced the following probability distribution of the number of times a student walks into the library over the period of a semester.Find the following probabilities.a. P(X ≥ 20)b. P(X = 60)c. P(X > 50)d. P(X >100)
After analyzing the frequency with which cross-country skiers participate in their sport, a sports-writer created the following probability distribution for X = number of times per year cross-country skiers ski.Find the following.a. P(3)b. P(X ≥ 5)c. P(5 ≤ X ≤7)
The natural remedy echinacea is reputed to boost the immune system, which will reduce the number of flu and colds. A 6-month study was undertaken to determine whether the remedy works. From this study, the following probability distribution of the number of respiratory infections per year (X) for
A shopping mall estimates the probability distribution of the number of stores mall customers actually enter, as shown in the table.Find the mean and standard deviation of the number of storesentered.
Refer to Exercise 7.30. Suppose that, on average, customers spend 10 minutes in each store they enter. Find the mean and standard deviation of the total amount of time customers spend in stores.
When parking a car in a downtown parking lot, drivers pay according to the number of hours or parts thereof. The probability distribution of the number of hours cars are parked has been estimated as follows.Find the mean and standard deviation of the number of hours cars are parked in thelot.
Refer to Exercise 7.32. The cost of parking is $2.50 per hour. Calculate the mean and standard deviation of the amount of revenue each car generates.
The manager of a bookstore recorded the number of customers who arrive at a checkout counter every 5 minutes from which the following distribution was calculated. Calculate the mean and standard deviation of the randomvariable.
It cost one dollar to buy a lottery ticket, which has five prizes. The prizes and the probability that a player wins the prize are listed here. Calculate the expected value of thepayoff.
After an analysis of incoming faxes, the manager of an accounting firm determined the probability distribution of the number of pages per facsimile as follows:Compute the mean and variance of the number of pages perfax.
Refer to Exercise 7.38. Further analysis by the manager revealed that the cost of processing each page of a fax is $.25. Determine the mean and variance of the cost per fax.
When food is irradiated with gamma rays from a cobalt-60 source, does the food become radioactive? Defend your answer.
Suppose Star A is four times as luminous as Star B. If these stars are both 500 light years away from Earth, how will their apparent brightness compare? How will the apparent brightness of these stars compare if Star A is twice as far away as Star B?
Why did ancient cultures study the constellations?
Why are the long-wavelength microwaves that permeate the universe considered to be evidence of the Big Bang?
Why is there a lower limit on the mass of a star? Why is there an upper limit to the mass of a star?
We see the constellations as distinct groups of stars. Discuss why they would look entirely different from some other location in the universe, far distant from Earth.
Why are the inner planets rocky while the outer planets are gaseous?
Why are the seasons on Uranus different from the seasons on any other planet?
Refer to Exercise 7.54. Find the following conditional probabilities.a. P(1 refrigerator ∣ 0 stoves)b. P(0 stoves ∣ 1 refrigerator)c. P(2 refrigerators ∣ 2 stoves)
There are four activities along the critical path for a project. The expected values and variances of the completion times of the activities are listed here. Determine the expected value and variance of the completion time of theproject.
The operations manager of a large plant wishes to overhaul a machine. After conducting a PERT/CPM analysis he has developed the following critical path.1. Disassemble machine2. Determine parts that need replacing3. Find needed parts in inventory4. Reassemble machine5. Test machineHe has estimated
In preparing to launch a new product, a marketing manager has determined the critical path for her department. The activities and the mean and variance of the completion time for each activity along the critical path are shown in the accompanying table. Determine the mean and variance of the
A professor of business statistics is about to begin work on a new research project. Because his time is quite limited, he has developed a PERT/CPM critical path, which consists of the following activities:1. Conduct a search for relevant research articles.2. Write a proposal for a research
A portfolio is composed of two stocks. The proportion of each stock, their expected values, and standard deviations are listed next.For each of the following coefficients of correlation, calculate the expected value and standard deviation of the portfolio:a. ρ = .5b. ρ = .2c. ρ = 0
An investor is given the following information about the returns on two stocks:a. If he is most interested in maximizing his returns, which stock should he choose?b. If he is most interested in minimizing his risk, which stock should hechoose?
Refer to Exercise 7.63. Compute the expected value and standard deviation of the portfolio composed of 60% stock 1 and 40% stock 2. The coefficient of correlation is .4.An investor is given the following information about the returns on twostocks:
Refer to Exercise 7.63. Compute the expected value and standard deviation of the portfolio composed of 30% stock 1 and 70% stock 2.An investor is given the following information about the returns on twostocks:
Given a binomial random variable with n = 10 and p = .3, use the formula to find the following probabilities.a. P(X = 3)b. P(X = 5)c. P(X = 8)
Repeat Exercise using Table 1 in Appendix B.In Exercise, given a binomial random variable with n = 10 and p = .3, use the formula to find the following probabilities.a. P(X = 3)b. P(X = 5)c. P(X = 8)
Given a binomial random variable with n = 6 and p = .2, use the formula to find the following probabilities.a. P(X = 2)b. P(X = 3)c. P(X = 5)
Repeat Exercise using Table 1 in Appendix B.Given a binomial random variable with n = 6 and p = .2, use the formula to find the following probabilities.a. P(X = 2)b. P(X = 3)c. P(X = 5)
Suppose X is a binomial random variable with n = 25 and p = .7. Use Table 1 to find the following.a. P(X = 18)b. P(X = 15)c. P(X ≤ 20)d. P(X ≥ 16)
A sign on the gas pumps of a chain of gasoline stations encourages customers to have their oil checked with the claim that one out of four cars needs to have oil added. If this is true, what is the probability of the following events?a. One out of the next four cars needs oilb. Two out of the next
A certain type of tomato seed germinates 90% of the time. A backyard farmer planted 25 seeds.a. What is the probability that exactly 20 germinate?b. What is the probability that 20 or more germinate?c. What is the probability that 24 or fewer germinate?d. What is the expected number of seeds that
In the United States, voters who are neither Democrat nor Republican are called Independents. It is believed that 10% of all voters are Independents. A survey asked 25 people to identify themselves as Democrat, Republican, or Independent.a. What is the probability that none of the people are
In the game of blackjack as played in casinos in Las Vegas, Atlantic City, and Niagara Falls, as well as in many other cities, the dealer has the advantage. Most players do not play very well. As a result, the probability that the average player wins a hand is about 45%. Find the probability that
Several books teach blackjack players the “basic strategy,” which increases the probability of winning any hand to 50%. Repeat Exercise, assuming the player plays the basic strategy.In Exercise, in the game of blackjack as played in casinos in Las Vegas, Atlantic City, and Niagara Falls, as
The best way of winning at blackjack is to “case the deck,” which involves counting 10s, non-10s, and aces. For card counters, the probability of winning a hand may increase to 52%. Repeat Exercise for a card counter.In Exercise, in the game of blackjack as played in casinos in Las Vegas,
According to a Gallup Poll conducted March 5−7, 2001, 52% of American adults think that protecting the environment should be given priority over developing U.S. energy supplies. Thirty-six percent think that developing energy supplies is more important, and 6% believe the two are equally
In a Bon Appetit poll, 38% of people said that chocolate was their favorite flavor of ice cream. A sample of 20 people was asked to name their favorite flavor of ice cream. What is the probability that half or more of them prefer chocolate?
The statistics practitioner in Exercise also determined that if a batter hits a line drive, the probability of an out is .23. Determine the following probabilities.a. In a game with 10 line drives, at least 5 are outs.b. In a game with 25 line drives, there are 5 outs or less.
According to the last census, 45% of working women held full-time jobs in 2002. If a random sample of 50 working women is drawn, what is the probability that 19 or more hold full-time jobs?
Given a Poisson random variable with μ = 2, use the formula to find the following probabilities.a. P(X = 0)b. P(X = 3)c. P(X = 5)
Given that X is a Poisson random variable with μ = .5, use the formula to determine the following probabilities.a. P(X = 0)b. P(X = 1)c. P(X = 2)
The number of accidents that occur at a busy intersection is Poisson distributed with a mean of 3.5 per week. Find the probability of the following events.a. No accidents in one weekb. Five or more accidents in one weekc. One accident today
Snowfalls occur randomly and independently over the course of winter in a Minnesota city. The average is one snowfall every 3 days.a. What is the probability of five snowfalls in 2 weeks?b. Find the probability of a snowfall today.
The number of students who seek assistance with their statistics assignments is Poisson distributed with a mean of two per day.a. What is the probability that no students seek assistance tomorrow?b. Find the probability that 10 students seek assistance in a week.
Hits on a personal website occur quite infrequently.They occur randomly and independently with an average of five per week.a. Find the probability that the site gets 10 or more hits in a week.b. Determine the probability that the site gets 20 or more hits in 2 weeks.
In older cities across North America, infrastructure is deteriorating, including water lines that supply homes and businesses. A report to the Toronto city council stated that there are on average 30 water line breaks per 100 kilometers per year in the city of Toronto. Outside of Toronto, the
The number of bank robberies that occur in a large North American city is Poisson distributed with a mean of 1.8 per day. Find the probabilities of the following events.a. Three or more bank robberies in a dayb. Between 10 and 15 (inclusive) robberies during a 5-day period
Flaws in a carpet tend to occur randomly and independently at a rate of one every 200 square feet. What is the probability that a carpet that is 8 feet by10 feet contains no flaws?
Complaints about an Internet brokerage firm occur at a rate of five per day. The number of complaints appears to be Poisson distributed.a. Find the probability that the firm receives 10 or more complaints in a day.b. Find the probability that the firm receives 25 or more complaints in a 5-day
The number of trucks crossing at the Ambassador Bridge connecting Detroit, Michigan, and Windsor, Ontario, is Poisson distributed with a mean of 1.5 per minute.a. What is the probability that in any 1-minute time span two or more trucks will cross the bridge?b. What is the probability that fewer
Cars arriving for gasoline at a particular gas station follow a Poisson distribution with a mean of 5 per hour.a. Determine the probability that over the next hour only one car will arrive.b. Compute the probability that in the next 3 hours more than 20 cars will arrive.
The number of users of an automatic banking machine is Poisson distributed. The mean number of users per 5-minute interval is 1.5. Find the probability of the following events.a. No users in the next 5 minutesb. Five or fewer users in the next 15 minutesc. Three or more users in the next 10 minutes
In 2000, Northwest Airlines boasted that 77.4% of its flights were on time. If we select five Northwest flights at random, what is the probability that all five are on time?
The final exam in a one-term statistics course is taken in the December exam period. Students who are sick or have other legitimate reasons for missing the exam are allowed to write a deferred exam scheduled for the first week in January. A statistics professor has observed that only 2% of all
In what ways can sea level be lowered? What effect might the lowering of sea level have on existing life forms?
The number of arrivals at a car wash is Poisson distributed with a mean of eight per hour.a. What is the probability that 10 cars will arrive in the next hour?b. What is the probability that more than 5 cars will arrive in the next hour?c. What is the probability that fewer than 12 cars will arrive
The percentage of customers who enter a restaurant and ask to be seated in a smoking section is 15%. Suppose that 100 people enter the restaurant.a. What is the expected number of people who request a smoking table?b. What is the standard deviation of the number of requests for a smoking table?c.
Lotteries are an important income source for various governments around the world. However, the availability of lotteries and other forms of gambling have created a social problem: gambling addicts. A critic of government-controlled gambling contends that 30% of people who regularly buy
The distribution of the number of home runs in soft-ball games is shown here.a. Calculate the mean number of home runs.b. Find the standarddeviation.
An auditor is preparing for a physical count of inventory as a means of verifying its value. Items counted are reconciled with a list prepared by the storeroom supervisor. In one particular firm, 20% of the items counted cannot be reconciled without reviewing invoices. The auditor selects 10 items.
Shutouts in the National Hockey League occur randomly and independently at a rate of 1 every 20 games. Calculate the probability of the following events.a. 2 shutouts in the next 10 gamesb. 25 shutouts in 400 gamesc. A shutout in to, night’s game
Most Miami Beach restaurants offer “early-bird” specials. These are lower-priced meals that are available only from 4 to 6 p.m. However, not all customers who arrive between 4 and 6 p.m. order the special. In fact, only 70% do.a. Find the probability that of 80 customers between 4 and 6 p.m.,
According to climatologists, the long-term average for Atlantic storms is 9.6 per season (June 1 to November 30), with 6 becoming hurricanes and 2.3 becoming intense hurricanes. Find the probability of the following events.a. Ten or more Atlantic stormsb. Five or fewer hurricanesc. Three or more
Researchers at the University Of Pennsylvania School Of Medicine theorized that children under 2 years old who sleep in rooms with the light on have a 40% probability of becoming myopic by age 16. Suppose that researchers found 25 children who slept with the light on before they were 2.a. What is
A pharmaceutical researcher working on a cure for baldness noticed that middle-aged men who are balding at the crown of their head have a 45% probability of suffering a heart attack over the next decade. In a sample of 100 middle-age balding men, what are the following probabilities?a. More than 50
According to the U.S. census, one-third of all businesses are owned by women. If we select 25 businesses at random, what is the probability that 10 or more of them are owned by women?
It is recommended that women age 40 and older have a mammogram annually. A recent report indicated that if a woman has annual mammograms over a 10-year period, there is a 60% probability that there will be at least one false-positive result. (A false-positive mammogram test result is one that
In a recent election, the mayor received 60% of the vote. Last week, a survey was undertaken that asked 100 people whether they would vote for the mayor. Assuming that her popularity has not changed, what is the probability that more than 50 people in the sample would vote for the mayor?
When Earth traveled through the storm of meteorites trailing the comet Tempel-Tuttle on November 17, 1998, the storm was 1,000 times as intense as the average meteor storm. Before the comet arrived, telecommunication companies worried about the potential damage that might be inflicted on the
In a recent census, the number of color televisions per household was recordeda. Develop the probability distribution of X, the number of color televisions per household.b. Determine the following probabilities.P1X ≤ 22P(X > 2)P1X ≥ 42
Using historical records, the personnel manager of a plant has determined the probability distribution of X, the number of employees absent per day. It isa. Find the following probabilities.P12 ≤ X ≤ 52P(X > 5)P(X < 4)b. Calculate the mean of the population.c. Calculate the standard deviation
Use a probability tree to compute the probability of the following events when flipping two fair coins.a. Heads on the first coin and heads on the second coinb. Heads on the first coin and tails on the second coinc. Tails on the first coin and heads on the second coind. Tails on the first coin and
Draw a probability tree to describe the flipping of three fair coins.
Refer to Exercise 7.16. Find the following probabilities.a. Two headsb. One headc. At least one headd. At least two heads
The random variable X has the following distribution.a. Find the mean and variance for the probability distribution below.b. Determine the probability distribution of Y where Y = 5X.c. Use the probability distribution in part (b) to compute the mean and variance of Y.d. Use the laws of expected
We are given the following probability distribution.a. Calculate the mean, variance, and standard deviation.b. Suppose that Y = 3X + 2. For each value of X, determine the value of Y. What is the probability distribution of Y?c. Calculate the mean, variance, and standard deviation from the
Refer to Exercise 7.22. Determine the mean and variance of the number of games played.
The joint probability distribution of X and Y is shown in the following table.a. Determine the marginal distributions of X and Y.b. Compute the covariance and coefficient of correlation between X and Y.c. Develop the probability distribution of X +Y.
The following distributions of X and of Y have been developed. If X and Y are independent, determine the joint probability distribution of X andY.
The distributions of X and of Y are described here. If X and Y are independent, determine the joint probability distribution of X andY.
After analyzing several months of sales data, the owner of an appliance store produced the following joint probability distribution of the number of refrigerators and stoves sold daily.a. Find the marginal probability distribution of the number of refrigerators sold daily.b. Find the marginal
Canadians who visit the United States often buy liquor and cigarettes, which are much cheaper in the United States. However, there are limitations. Canadians visiting in the United States for more than 2 days are allowed to bring into Canada one bottle of liquor and one carton of cigarettes. A
a. American Express (AXP) (20%), Bank of America (BAC) (30%), JP Morgan Chase (JPM) (50%)b. AXP (20%), BAC (60%), JPM (20%)c. AXP (50%), BAC (30%), JPM (20%)d. Which portfolio would an investor who likes to gamble choose? Explain.e. Which portfolio would a risk-averse investor choose? Explain.We
a. Alcoa (AA) (25%), Home Depot (HD) (25%), International Business Machines (IBM) (25%), Travelers (TRV) (25%)b. AA (10%), HD (50%), IBM (20%), TRV (20%)c. AA (30%), HD (20%), IBM (10%), TRV (40%)d. Which portfolio would a gambler choose? Explain.e. Which portfolio would a risk-averse investor
a. Cisco Systems (CSCO)(25%), Disney (DIS) (25%), General Electric (GE) (25%), Wal-Mart Stores (WMT) (25%)b. CSCO (10%), DIS (20%), GE (30%), WMT (40%)c. CSCO (55%), DIS (15%), GE (15%), WMT (15%)d. Explain why the choice of which portfolio to invest in is obvious.We have recorded the monthly
a. Boeing (BA) (25%), Caterpillar (CAT) (25%), Chevron (CVX) (25%), Coca-Cola (KO) (25%)b. BA (10%), CAT (20%), CVX (20%), KO (50%)c. BA (15%), CAT (55%), CVX (15%), KO (15%)d. Which portfolio would a gambler choose? Explain.e. Which portfolio would a risk-averse investor choose? Explain.We have
a. Du Pont (DD) (25%), Exxon (XOM) (25%), Verizon Communications (VZ), (25%), Intel (INTC) (25%)b. DD (40%), XOM (30%), VZ (20%), INTC (10%)c. DD (10%), XOM (20%), VZ (30%), INTC (40%)d. Which portfolio would a gambler choose? Explain.e. Which portfolio would a risk-averse investor choose?
a. Johnson & Johnson (JNJ) (25%), McDonald’s (MCD) (25%), Merck (MRK) (25%), Microsoft (MSFT) (25%)b. JNJ (10%), MCD (30%), MRK (10%), MSFT (50%)c. JNJ (10%), MCD (70%), MRK (10%), MSFT (0%)d. Explain why the choice of which portfolio to invest in is obvious.We have recorded the monthly returns
a. Pfizer (PFE) (25%), Proctor & Gamble (PG) (25%), United Technologies (UTX) (25%), United Health (UNH) (25%)b. PFE (40%), PG (30%), UTX (20%), UNH (10%)c. PFE (15%), PG (55%), UTX (15%), UNH (15%)d. Which portfolio would a gambler choose? Explain.e. Which portfolio would a risk-averse investor
a. Barrick Gold (ABX) (25%), Bombardier (BBD.B) (25%), Bell Canada Enterprises (BCE) (25%), Bank of Montreal (BMO) (25%)b. ABX (50%), BBD.B (10%), BCE (10%), BMO (30%)c. ABX (10%), BBD.B (40%), BCE (40%), BMO (10%)d. Which portfolio would a gambler choose? Explain.e. Which portfolio would a
a. Rogers Communication (RCI.B) (25%), Royal Bank of Canada (RY) (25%), Shaw Communications (SJR.B) (25%), Suncor Energy (SU) (25%)b. RCI.B (10%), RY (50%), SJR.B (30%), (SU) (10%)c. RCI.B (20%), RY (40%), SJR.B (30%), (SU) (10%)d. Which portfolio would a gambler choose? Explain.e. Which portfolio
a. Canadian Imperial Bank of Commerce (CM) (25%), Enbridge (ENB) (25%), Potash Corporation of Saskatchewan (POT) (25%), Power Corporation of Canada (POW) (25%),b. CM (15%), ENB (55%), POT (15%), POW (15%)c. CM (10%), ENB (20%), POT (30%), POW (40%)d. Explain why the choice of which portfolio to
a. Bank of Nova Scotia (BNS) (25%), Canadian National Railways (CNR) (25%), (25%), Canadian Tire (CTC.A) (25%), Magna International (MG) (25%)b. BNS (20%), CNR (60%), CTC.A (10%), MG (10%)c. BNS (40%), CNR (30%), CTC.A (20%), MG (10%)d. Explain why the choice of which portfolio to invest in is
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