Compute the mean and variance of the following discrete

Basic Statistics for Business and Economics | 7th Edition | ISBN: 9780077384470 | Authors: Douglas Lind; William Marchal; Samuel Wathen

Chapter 6: Problem 60 Basic Statistics for Business and Economics 7

Problem 60E Refer to the Real Estate data, which report information on homes sold in the Denver, Colorado, area last year. a. Create a probability distribution for the number of bedrooms. Compute the mean and the standard deviation of this distribution. ________________ b. Create a probability distribution for the number of bathrooms. Compute the mean and the standard deviation of this distribution.

Chapter 6: Problem 1 Basic Statistics for Business and Economics 7

Problem 1E Compute the mean and variance of the following discrete probability distribution. x P(x) 0 .2 1 .4 2 .3 3 .1

Chapter 6: Problem 4 Basic Statistics for Business and Economics 7

Problem 4E Which of these variables are discrete and which are continuous random variables? a. The number of new accounts established by a salesperson in a year. ________________ b. The time between customer arrivals to a bank ATM. ________________ c. The number of customers in Big Nick’s barber shop. ________________ d. The amount of fuel in your car’s gas tank. ________________ e. The number of minorities on a jury. ________________ f. The outside temperature today.

Chapter 6: Problem 2 Basic Statistics for Business and Economics 7

Problem 2E Compute the mean and variance of the following discrete probability distribution. x P(x) 2 .5 8 .3 10 .2

Chapter 6: Problem 5 Basic Statistics for Business and Economics 7

The information below is the number of daily emergency service calls made by the volunteer ambulance service of Walterboro, South Carolina, for the last 50 days. To explain, there were 22 days on which there were 2 emergency calls, and 9 days on which there were 3 emergency calls. a. Convert this information on the number of calls to a probability distribution. b. Is this an example of a discrete or continuous probability distribution? c. What is the mean number of emergency calls per day? d. What is the standard deviation of the number of calls made daily?

Chapter 6: Problem 3 Basic Statistics for Business and Economics 7

Problem 3E Three tables listed at the top of page 190 show “random variables” and their “probabilities.” However, only one of these is actually a probability distribution. a. Which is it? x P(x) 5 .3 10 .3 15 .2 20 .4 X P(x) 5 .1 10 .3 15 .2 20 .4 X P(x) 5 .5 10 .3 15 ?.2 20 .4 ________________ b. Using the correct probability distribution, find the probability that x is: (1) Exactly 15. (2) No more than 10. (3) More than 5. ________________ c. Compute the mean, variance, and standard deviation of this distribution.

Chapter 6: Problem 6 Basic Statistics for Business and Economics 7

The director of admissions at Kinzua University in Nova Scotia estimated the distribution of student admissions for the fall semester on the basis of past experience. What is the expected number of admissions for the fall semester? Compute the variance and the standard deviation of the number of admissions. Admissions Probability 1,000 .6 1,200 .3 1,500 .1

Chapter 6: Problem 7 Basic Statistics for Business and Economics 7

Problem 7E Belk Department Store is having a special sale this weekend. Customers charging purchases of more than $50 to their Belk credit card will be given a special Belk Lottery card. The customer will scratch off the card, which will indicate the amount to be taken off the total amount of the purchase. Listed below are the amount of the prize and the percent of the time that amount will be deducted from the total amount of the purchase. Prize Amount Probability $10 .50 25 .40 50 .08 100 .02 a. What is the mean amount deducted from the total purchase amount? ________________ b. What is the standard deviation of the amount deducted from the total purchase?

Chapter 6: Problem 8 Basic Statistics for Business and Economics 7

Problem 8E The Downtown Parking Authority of Tampa, Florida, reported the following information for a sample of 250 customers on the number of hours cars are parked and the amount they are charged. Number of Hours Frequency Amount Charged 1 20 $ 3.00 2 38 6.00 3 53 9.00 4 45 12.00 5 40 14.00 6 13 16 00 7 5 18.00 8 36 18.00 250 a. Convert the information on the number of hours parked to a probability distribution. Is this a discrete or a continuous probability distribution? ________________ b. Find the mean and the standard deviation of the number of hours parked. How would you answer the question: How long is a typical customer parked? ________________ c. Find the mean and the standard deviation of the amount charged.

Chapter 6: Problem 9 Basic Statistics for Business and Economics 7

Problem 9E In a binomial situation n = 4 and ? = .25. Determine the probabilities of the following events using the binomial formula. a. x = 2 ________________ b. x = 3

Chapter 6: Problem 10 Basic Statistics for Business and Economics 7

Problem 10E In a binomial situation n = 5 and ? = .40. Determine the probabilities of the following events using the binomial formula. a. x = 1 ________________ b. x= 2

Chapter 6: Problem 11 Basic Statistics for Business and Economics 7

Problem 11E Assume a binomial distribution where n = 3 and ? = .60. a. Refer to Appendix B.9, and fist the probabilities for values of x from 0 to 3. ________________ b. Determine the mean and standard deviation of the distribution from the general definitions given in formulas (6–1) and (6–2).

Chapter 6: Problem 12 Basic Statistics for Business and Economics 7

Problem 12E Assume a binomial distribution where n = 5 and ? = .30. a. Refer to Appendix B.9, and list the probabilities for values of x from 0 to 5. ________________ b. Determine the mean and standard deviation of the distribution from the general definitions given in formulas (6–1) and (6–2).

Chapter 6: Problem 13 Basic Statistics for Business and Economics 7

Problem 13E An American Society of Investors survey found 30 percent of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability: a. Exactly two of the sampled individuals have used a discount broker? ________________ b. Exactly four of them have used a discount broker? ________________ c. None of them have used a discount broker?

Chapter 6: Problem 14 Basic Statistics for Business and Economics 7

Problem 14E The United States Postal Service reports 95 percent of first class mail within the same city is delivered within two days of the time of mailing. Six letters are randomly sent to different locations. a. What is the probability that all six arrive within two days? ________________ b. What is the probability that exactly five arrive within two days? ________________ c. Find the mean number of letters that will arrive within two days. ________________ d. Compute the variance and standard deviation of the number that will arrive within two days.

Chapter 6: Problem 15 Basic Statistics for Business and Economics 7

Problem 15E Industry standards suggest that 10 percent of new vehicles require warranty service within the first year. Jones Nissan in Sumter, South Carolina, sold 12 Nissans yesterday. a. What is the probability that none of these vehicles requires warranty service? ________________ b. What is the probability exactly one of these vehicles requires warranty service? ________________ c. Determine the probability that exactly two of these vehicles require warranty service. ________________ d. Compute the mean and standard deviation of this probability distribution.

Chapter 6: Problem 16 Basic Statistics for Business and Economics 7

Problem 16E A telemarketer makes six phone calls per hour and is able to make a sale on 30 percent of these contacts. During the next two hours, find: a. The probability of making exactly four sales. ________________ b. The probability of making no sales. ________________ c. The probability of making exactly two sales. ________________ d. The mean number of sales in the two-hour period.

Chapter 6: Problem 18 Basic Statistics for Business and Economics 7

Problem 18E It is reported that 16 percent of American households use a cell phone exclusively for their telephone service. In a sample of eight households, find the probability that: a. None use a cell phone as their exclusive service. ________________ b. At least one uses the cell exclusively. ________________ c. At least five use the cell phone.

Chapter 6: Problem 19 Basic Statistics for Business and Economics 7

Problem 19E In a binomial distribution n = 8 and ? = .30. Find the probabilities of the following events. a. x = 2. ________________ b. x ? 2 (the probability that x is equal to or less than 2). ________________ c. x ? 3 (the probability that x is equal to or greater than 3).

Chapter 6: Problem 17 Basic Statistics for Business and Economics 7

Problem 17E A recent survey by the American Accounting Association revealed 23 percent of students graduating with a major in accounting select public accounting. Suppose we select a sample of 15 recent graduates. a. What is the probability two select public accounting? ________________ b. What is the probability five select public accounting? ________________ c. How many graduates would you expect to select public accounting?

Chapter 6: Problem 20 Basic Statistics for Business and Economics 7

Problem 20E In a binomial distribution n = 12 and ? = .60. Find the following probabilities. a. x = 5. ________________ b. x ? 5. ________________ c. x ? 6.

Chapter 6: Problem 21 Basic Statistics for Business and Economics 7

In a recent study 90 percent of the homes in the United States were found to have large- screen TVs. In a sample of nine homes, what is the probability that: a. All nine have large-screen TVs? b. Less than five have large-screen TVs? c. More than five have large-screen TVs? d. At least seven homes have large-screen TVs?

Chapter 6: Problem 22 Basic Statistics for Business and Economics 7

Problem 22E A manufacturer of window frames knows from long experience that 5 percent of the production will have some type of minor defect that will require an adjustment. What is the probability that in a sample of 20 window frames: a. None will need adjustment? ________________ b. At least one will need adjustment? ________________ c. More than two will need adjustment?

Chapter 6: Problem 23 Basic Statistics for Business and Economics 7

Problem 23E The speed with which utility companies can resolve problems is very important. GTC, the Georgetown Telephone Company, reports it can resolve customer problems the same day they are reported in 70 percent of the cases. Suppose the 15 cases reported today are representative of all complaints. a. How many of the problems would you expect to be resolved today? What is the standard deviation? ________________ b. What is the probability 10 of the problems can be resolved today? ________________ c. What is the probability 10 or 11 of the problems can be resolved today? ________________ d. What is the probability more than 10 of the problems can be resolved today?

Chapter 6: Problem 24 Basic Statistics for Business and Economics 7

Problem 24E It is asserted that 80 percent of the cars approaching an individual toll both in New Jersey are equipped with an E-ZPass transponder. Find the probability that in a sample of six cars: a. All six will have the transponder. ________________ b. At least three will have the transponder. ________________ c. None will have a transponder.

Chapter 6: Problem 26 Basic Statistics for Business and Economics 7

Problem 26E In a Poisson distribution µ = 4. a. What is the probability that x = 2? ________________ b. What is the probability that x ? 2? ________________ c. What is the probability that x> 2?

Chapter 6: Problem 27 Basic Statistics for Business and Economics 7

Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans. a. What is the probability that 3 loans will be defaulted? b. What is the probability that at least 3 loans will be defaulted?

Chapter 6: Problem 25 Basic Statistics for Business and Economics 7

Problem 25E In a Poisson distribution µ = 0.4. a. What is the probability that x = 0? ________________ b. What Is the probability that x > 0?

Chapter 6: Problem 28 Basic Statistics for Business and Economics 7

Problem 28E Automobiles arrive at the Elkhart exit of the Indiana Toll Road at the rate of two per minute. The distribution of arrivals approximates a Poisson distribution. a. What is the probability that no automobiles arrive in a particular minute? ________________ b. What is the probability that at least one automobile arrives during a particular minute?

Chapter 6: Problem 29 Basic Statistics for Business and Economics 7

It is estimated that 0.5 percent of the callers to the Customer Service department of Dell, Inc., will receive a busy signal. What is the probability that of today's 1,200 callers, at least 5 received a busy signal?

Chapter 6: Problem 30 Basic Statistics for Business and Economics 7

Problem 30E In the past, schools in Los Angeles County have closed an average of three days each year for weather emergencies. What is the probability that schools in Los Angeles County will close for four-days next year?

Chapter 6: Problem 31 Basic Statistics for Business and Economics 7

Problem 31E What is the difference between a random variable and a probability distribution?

Chapter 6: Problem 32 Basic Statistics for Business and Economics 7

Problem 32E For each of the following indicate whether the random variable is discrete or continuous. a. The length of time to get a haircut. ________________ b. The number of cars a jogger passes each morning while running. ________________ c. The number of hits for a team in a high school girls’ softball game. ________________ d. The number of patients treated at the South Strand Medical Center between 6 and 10 p.m. each night. ________________ e. The distance your car traveled on the last fill-up. ________________ f. The number of customers at the Oak Street Wendy’s who used the drive-through facility. ________________ g. The distance between Gainesville, Florida, and all Florida cities with a population of at least 50,000.

Chapter 6: Problem 33 Basic Statistics for Business and Economics 7

Problem 33E An investment will be worth $1,000, $2,000, or $5,000 at the end of the year. The probabilities of these values are .25, .60, and .15, respectively. Determine the mean and variance of the worth of the investment.

Chapter 6: Problem 34 Basic Statistics for Business and Economics 7

Problem 34E The personnel manager of Cumberland Pig Iron Company is studying the number of on- the-job accidents over a period of one month. He developed the following probability distribution. Compute the mean, variance, and standard deviation of the number of accidents in a month. Number of Accidents Probability 0 .40 1 .20 2 .20 3 .10 4 .10

Chapter 6: Problem 35 Basic Statistics for Business and Economics 7

Problem 35E Croissant Bakery, Inc., offers special decorated cakes for birthdays, weddings, and other occasions. It also has regular cakes available in its bakery. The following table gives the total number of cakes sold per day and the corresponding probability. Compute the mean, variance, and standard deviation of the number of cakes sold per day. Number of Cakes Sold in a Day Probability 12 .25 13 .40 14 .25 15 .10

Chapter 6: Problem 36 Basic Statistics for Business and Economics 7

Problem 36E The payouts for the Powerball lottery and their corresponding odds and probabilities of occurrence are shown below. The price of a ticket is $1.00. Find the mean and standard deviation of the payout. Hint: Don’t forget to include the cost of the ticket and its corresponding probability. Divisions Payout Odds Probability Five plus Powerball $50,000,000 146,107,962 0.000000006844 Match 5 200,000 3,563,609 0.000000280614 Four plus Powerball 10,000 584,432 0.000001711060 Match 4 100 14,255 0.000070145903 Three plus Powerball 100 11,927 0.000083836351 Match 3 7 291 0.003424657534 Two plus Powerball 7 745 0.001340482574 One plus Powerball 4 127 0.007812500000 Zero plus Powerball 3 69 0.014285714286

Chapter 6: Problem 37 Basic Statistics for Business and Economics 7

Problem 37E In a recent survey 35 percent indicated chocolate was their favorite flavor of ice cream. Suppose we select a sample of ten people and ask them to name their favorite flavor of ice cream. a. How many of those in the sample would you expect to name chocolate? ________________ b. What is the probability exactly four of those in the sample name chocolate? ________________ c. What is the probability four or more name chocolate?

Chapter 6: Problem 38 Basic Statistics for Business and Economics 7

Problem 38E Thirty percent of the population in a southwestern community are Spanish-speaking Americans. A Spanish-speaking person is accused of killing a non-Spanish-speaking American and goes to trial. Of the first 12 potential jurors, only 2 are Spanish-speaking Americans, and 10 are not. The defendant’s lawyer challenges the jury selection, claiming bias against her client. The government lawyer disagrees, saying that the probability of this particular jury composition is common. Compute the probability and discuss the assumptions.

Chapter 6: Problem 39 Basic Statistics for Business and Economics 7

Problem 39E An auditor for Health Maintenance Services of Georgia reports 40 percent of policyholders 55 years or older submit a claim during the year. Fifteen policyholders are randomly selected for company records. a. How many of the policyholders would you expect to have filed a claim within the last year? ________________ b. What is the probability that 10 of the selected policyholders submitted a claim last year? ________________ c. What is the probability that 10 or more of the selected policyholders submitted a claim last year? ________________ d. What is the probability that more than 10 of the selected policyholders submitted a claim last year?

Chapter 6: Problem 40 Basic Statistics for Business and Economics 7

Problem 40E Tire and Auto Supply is considering a 2-for-1 stock split. Before the transaction is finalized, at least two-thirds of the 1,200 company stockholders must approve the proposal. To evaluate the likelihood the proposal will be approved, the CFO selected a sample of 18 stockholders. He contacted each and found 14 approved of the proposed split. What is the likelihood of this event, assuming two-thirds of the stockholders approve?

Chapter 6: Problem 41 Basic Statistics for Business and Economics 7

Problem 41E A federal study reported that 7.5 percent of the U.S. workforce has a drug problem. A drug enforcement official for the State of Indiana wished to investigate this statement. In her sample of 20 employed workers: a. How many would you expect to have a drug problem? What is the standard deviation? ________________ b. What is the likelihood that none of the workers sampled has a drug problem? ________________ c. What is the likelihood at least one has a drug problem?

Chapter 6: Problem 42 Basic Statistics for Business and Economics 7

Problem 42E The Bank of Hawaii reports that 7 percent of its credit card holders will default at some time in their life. The Hiio branch just mailed out 12 new cards today. a. How many of these new cardholders would you expect to default? What is the standard deviation? ________________ b. What is the likelihood that none of the cardholders will default? ________________ c. What is the likelihood at least one will default?

Chapter 6: Problem 43 Basic Statistics for Business and Economics 7

Problem 43E Recent statistics suggest that 15 percent of those who visit a retail site on the World Wide Web make a purchase. A retailer wished to verify this claim. To do so, she selected a sample of 16 “hits” to her site and found that 4 had actually made a purchase. a. What is the likelihood of exactly four purchases? ________________ b. How many purchases should she expect? ________________ c. What is the likelihood that four or more “hits” result in a purchase?

Chapter 6: Problem 44 Basic Statistics for Business and Economics 7

Problem 44E In Chapter 19 we discuss the acceptance sample. Acceptance sampling is used to monitor the quality of incoming raw materials. Suppose a purchaser of electronic components allows 1 percent of the components to be defective. To ensure the quality of incoming parts, a purchaser or manufacturer normally samples 20 parts and allows 1 defect. a. What is the likelihood of accepting a lot that is 1 percent defective? ________________ b. If the quality of the incoming lot was actually 2 percent, what is the likelihood of accepting it? ________________ c. If the quality of the incoming lot was actually 5 percent, what is the likelihood of accepting it?

Chapter 6: Problem 45 Basic Statistics for Business and Economics 7

Problem 45E Colgate-Palmolive, Inc., recently developed a new toothpaste flavored with honey. It tested a group of ten people. Six of the group said they liked the new flavor, and the remaining four indicated they definitely did not. Four of the ten are selected to participate in an in-depth interview. What is the probability that of those selected for the in-depth interview two liked the new flavor and two did not?

Chapter 6: Problem 46 Basic Statistics for Business and Economics 7

Problem 46E Dr. Richmond, a psychologist, is studying the daytime television viewing habits of college students. She believes 45 percent of college students watch soap operas during the afternoon. To further investigate, she selects a sample of 10. a. Develop a probability distribution for the number of students in the sample who watch soap operas. ________________ b. Find the mean and the standard deviation of this distribution. ________________ c. What is the probability of finding exactly four watch soap operas? ________________ d. What is the probability less than half of the students selected watch soap operas?

Chapter 6: Problem 47 Basic Statistics for Business and Economics 7

Problem 47E A recent study conducted by Penn, Shone, and Borland, on behalf of LastMinute.com, revealed that 52 percent of business travelers plan their trips less than two weeks before departure. The study is to be replicated in the tri-state area with a sample of 12 frequent business travelers. a. Develop a probability distribution for the number of travelers who plan their trips within two weeks of departure. ________________ b. Find the mean and the standard deviation of this distribution. ________________ c. What is the probability exactly 5 of the 12 selected business travelers plan their trips within two weeks of departure? ________________ d. What is the probability 5 or fewer of the 12 selected business travelers plan their trips within two weeks of departure?

Chapter 6: Problem 48 Basic Statistics for Business and Economics 7

Problem 48E Most software manufacturers offer a free help line that allows customers to call an 800 number to receive assistance with their problems. Because of the volume of ca;;s, often customers are put on hold. Greeting Card Art, Inc. is proud of the fact that 93 percent of their calls for assistance directly by a techician who can solve the customer's problem, To monitor this service claim, suppose Greeting Card Art selects a random sample of 25 recent calls. a. Explain why this situation fits the binomial distribution.. ________________ b. What is the probaility exactly 20 of the calls are answered directly by a techician? ________________ c. What is the probability at least one of the calls is put on hold?

Chapter 6: Problem 49 Basic Statistics for Business and Economics 7

Problem 49E The sales of Lexus automobiles in the Detroit area follow a Poisson distribution with a mean of 3 per day. a. What is the probability that no Lexus is sold on a particular day? ________________ b. What is the probability that for five consecutive days at least one Lexus is sold?

Chapter 6: Problem 50 Basic Statistics for Business and Economics 7

Problem 50E Suppose 1.5 percent of the antennas on new Nokia cell phones are defective For a random sample of 200 antennas, find the probability that: a. None of the antennas is defective. ________________ b. Three or more of the antennas are defective.

Chapter 6: Problem 51 Basic Statistics for Business and Economics 7

Problem 51E A study of the checkout lines at the Safeway Supermarket in the South Strand area revealed that between 4 and 7 P.M. on weekdays there is an average of four customers waiting in line. What is the probability that you visit Safeway today during this period and find: a. No customers are waiting? ________________ b. Four customers are waiting? ________________ c. Four or fewer are waiting? ________________ d. Four or more are waiting?

Chapter 6: Problem 52 Basic Statistics for Business and Economics 7

Problem 52E An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two emails per hour. Assume the arrival of these emails is approximated by the Poisson distribution. a. What is the probability Linda Lahey, company president, received exactly 1 email between 4 P.M. and 5 P.M. yesterday? ________________ b. What is the probability she received 5 or more email during the same period? ________________ c. What is the probability she did not receive any email during the period?

Chapter 6: Problem 53 Basic Statistics for Business and Economics 7

Problem 53E Recent crime reports indicate that 3.1 motor vehicle thefts occur each minute in the United States. Assume that the distribution of thefts per minute can be approximated by the Poisson probability distribution. a. Calculate the probability exactly four thefts occur in a minute. ________________ b. What is the probability there are no thefts in a minute? ________________ c. What is the probability there is at least one theft in a minute?

Chapter 6: Problem 54 Basic Statistics for Business and Economics 7

Problem 54E New Process, Inc., a large mail-order supplier of women’s fashions, advertises sameday service on every order. Recently the movement of orders has not gone as planned, and there were a large number of complaints. Bud Owens, director of customer service, has completely redone the method of order handling. The goal is to have fewer than five unfilled orders on hand at the end of 95 percent of the working days. Frequent checks of the unfilled orders at the end of the day reveal that the distribution of the unfilled orders follows a Poisson distribution with a mean of two orders. a. Has New Process, Inc., lived up to its internal goal? Cite evidence. ________________ b. Draw a histogram representing the Poisson probability distribution of unfilled orders.

Chapter 6: Problem 55 Basic Statistics for Business and Economics 7

Problem 55E The National Aeronautics and Space Administration (NASA) has experienced two disasters. The Challenger exploded over the Atlantic Ocean in 1986 and the Columbia exploded over East Texas in 2003. There have been a total of 123 space missions. Assume failures continue to occur at the same rate and consider the next 23 missions. What is the probability of exactly two failures? What is the probability of no failures?

Chapter 6: Problem 56 Basic Statistics for Business and Economics 7

Problem 56E According to the “January theory,” if the stock market is up for the month of January, it will be up for the year. If it is down in January, it will be down for the year. According to an article in The Wall Street Journal, this theory held for 29 out of the last 34 years. Suppose there is no truth to this theory; that is, the probability it is either up or down is .50. What is the probability this could occur by chance? You will probably need a software package such as Excel or MINITAB.

Chapter 6: Problem 57 Basic Statistics for Business and Economics 7

Problem 57E During the second round of the 1989 U.S. Open golf tournament, four golfers scored a hole in one on the sixth hole. The odds of a professional golfer making a hole in one are estimated to be 3,708 to 1, so the probability is 1/3,709. There were 155 golfers participating in the second round that day. Estimate the probability that four golfers would score a hole in one on the sixth hole.

Chapter 6: Problem 58 Basic Statistics for Business and Economics 7

Problem 58E Suppose the National Hurricane Center forecasts that hurricanes will hit the strike area with a .95 probability. Answer the following questions: a. What probability distribution does this follow? ________________ b. What is the probability that 10 hurricanes reach landfall in the strike area? ________________ c. What is the probability at least one of 10 hurricanes reaches land outside the strike area?

Chapter 6: Problem 59 Basic Statistics for Business and Economics 7

Problem 59E A recent CBS News survey reported that 67 percent of adults felt the U.S. Treasury should continue making pennies. Suppose we select a sample of 15 adults. a. How many of the 15 would we expect to indicate that the Treasury should continue making pennies? What is the standard deviation? ________________ b. What is the likelihood that exactly 8 adults would indicate the Treasury should continue making pennies? ________________ c. What is the likelihood at least 8 adults would indicate the Treasury should continue making pennies?

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