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mathematics
statistics

Questions and Answers of Statistics

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
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
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.
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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,
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
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
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
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,
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
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 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.
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.
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
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
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
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
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 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
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
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
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
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.
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%
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
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
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
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.
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
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
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,
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,
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
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
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
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
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
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
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
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
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
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.
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.
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. 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
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.
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
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
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
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
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

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