Finite Math (20 Questions)
QUESTION 1The management of the Cambridge Company has projected the sales of its products (in millions of dollars) for the upcoming year, with the associated probabilities shown in the following table:SalesProbabilityWhat does the management expect the sales to be next year?a.18.7b.15.34c.28.98d.29.61e.32.341 pointsQUESTION 2The management of MultiVision, a cable TV company, intends to submit a bid for the cable television rights in one of two cities, A or B. If the company obtains the rights to city A, the probability of which is 0.3, the estimated profit over the next 10 yr is $10 million; if the company obtains the rights to city B, the probability of which is 0.4, the estimated profit over the next 10 yr is $7 million. The cost of submitting a bid for rights in city A is $300,000 and that of city B is $300,000.By comparing the expected profits for each venture, determine whether the company should bid for the rights in city A or city B.a.City Ab.City B1 pointsQUESTION 3In European roulette the wheel is divided into 37 compartments numbered 1 through 36 and 0. (In American roulette there are 38 compartments numbered 1 through 36, 0, and 00.) Find the expected value of the winnings on a $3 bet placed on red in European roulette. Round your answer to the nearest cent.a.$0.08%b.$0.03%c.- $0.03%d.- $0.08%1 pointsQUESTION 4Based on past experience, the manager of the VideoRama Store has compiled the following table, which gives the probabilities that a customer who enters the VideoRama Store will buy 0, 1, 2, 3, or 4 videocassettes. How many videocassettes can a customer entering this store be expected to buy?Video- cassettes01234Probability0.420.370.130.040.04a.E = 0.56b.E = 0.91c.E = 0.86d.E = 0.661 pointsQUESTION 5Find the expected value of a random variable X having the following probability distribution:x012345P(X = x)a.E( X) = 2.3125b.E( X) = 2.1875c.E( X) = 2.3825d.E( X) = 1.09751 pointsQUESTION 6If a player placed a $8 bet on red and a $5 bet on black in a single play in American roulette, what would be the expected value of his winnings? Round your answer to the nearest cent.a. centsb. centsc. centsd. centse. cents1 pointsQUESTION 7During the first year at a university that uses a 4-point grading system, a freshman took ten 3-credit courses and received one A, three Bs, two Cs, and four Ds.Compute this student’s grade point average.Let the random variable X denote the number of points corresponding to a given letter grade. Find the probability distribution of the random variable X and compute E( X), the expected value of X.a.2.1;x 1 2 3 4P (X = x) 1 3 2 4E(X) = 2.1b.2.9;x 1 2 3 4P (X = x) 0.4 0.2 0.3 0.1E(X) = 2.9c.2.9;x 1 2 3 4P (X = x) 0.1 0.3 0.2 0.4E(X) = 2.9d.2.1;x 1 2 3 4P (X = x) 0.4 0.2 0.3 0.1E(X) = 2.11 pointsQUESTION 8A woman purchased a $10,000, 1-year term-life insurance policy for $150. Assuming that the probability that she will live another year is 0.993, find the company’s expected gain.a.E = $90b.E = $100c.E = $140d.E = $801 pointsQUESTION 9Bob, the proprietor of Midland Lumber, feels that the odds in favor of a business deal going through are 7 to 6. What is the (subjective) probability that this deal will not materialize?a.0.4622b.0.4615c.0.4647d.0.44601 pointsQUESTION 10A buyer for Discount Fashions, an outlet for women’s apparel, is considering buying a batch of clothing for $61,000. She estimates that the company will be able to sell it for $80,000, $75,000, or $70,000 with probabilities of 0.20, 0.40, and 0.40, respectively.Based on these estimates, what will be the company’s expected gross profit?a.$10,400b.$23,400c.$13,000d.$7,800e.$15,600TWOQUESTION 1The probability distribution of a random variable X isx–2–1012P ( X = x )Compute the mean, variance, and standard deviation of X.a.b.c.d.1 pointsQUESTION 2A probability distribution has a mean of 57 and a standard deviation of 1.4. Use Chebychev’s inequality to find the value of c that guarantees the probability is at least 96% that an outcome of the experiment lies between 57 – c and 57 – c. (Round the answer to nearest whole number.)a.3b.9c.1d.7e.51 pointsQUESTION 3Find the variance of the probability distribution for the histogram:a.Var ( X) = 4.2625b.Var ( X) = 4.65c.Var ( X) = 4.28d.Var ( X) = 4.01251 pointsQUESTION 4The birthrates in the country for the years 1981-1990 are:Year1981198219831984198519861987198819891990Birthrate15.915.515.515.715.715.615.715.916.216.7(The birthrate is the number of live births/1,000 population.)Compute the mean, variance, and standard deviation of the random variable X.a.b.c.d.1 pointsQUESTION 5Rosa Walters is considering investing $10,000 in two mutual funds. The anticipated returns from price appreciation and dividends (in hundreds of dollars) are described by the following probability distributions:Mutual Fund AReturnsProbability-40.280.3100.5Mutual Fund BReturnsProbability-20.260.680.2Compute (in dollars) the mean and variance for each mutual fund.a.Mutual Fund A:Mutual Fund B:b.Mutual Fund A:Mutual Fund B:c.Mutual Fund A:Mutual Fund B:d.Mutual Fund A: Mutual Fund B:1 pointsQUESTION 6The number of Americans without health insurance, in millions, from 1995 through 2002 is summarized in the following table.Year19951996199719981999200020012002Americans40.541.443.644.7188.8.131.52What is the standard deviation of Americans without health insurance in the period from 1995 through 2002?a. millionb. millionc. milliond. millione. million1 pointsQUESTION 7The mean annual starting salary of a new graduate in a certain profession is $43,000 with a standard deviation of $500. What is the probability that the starting salary of a new graduate in this profession will be between $39,500 and $46,500?a.At leastb.At leastc.At leastd.At least1 pointsQUESTION 8A survey was conducted by the market research department of the National Real Estate Company among 500 prospective buyers in a large metropolitan area to determine the maximum price a prospective buyer would be willing to pay for a house. From the data collected, the distribution that follows was obtained.Compute the standard deviation of the maximum price (in thousands of dollars) that these buyers were willing to pay for a house. Round the answer to the nearest integer.Maximum Price Considered, 150160170180190220250270320a.b.c.d.e.1 pointsQUESTION 9The following table gives the scores of 30 students in a mathematics examination.Scores90-9980-8970-7960-6950-59Students381351Find the mean and the standard deviation of the distribution of the given data. Hint: Assume that all scores lying within a group interval take the midvalue of that group.a.b.c.d.e.1 pointsQUESTION 10A probability distribution has a mean of 45 and a standard deviation of 1. Use Chebychev’s inequality to estimate the probability that an outcome of the experiment lies between 43 and 47.a.At least 0.8b.At least 0.75c.At least 0.5d.At least 0.25e.At least 0.04
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