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If an alternative has a salvage value, how is it han- dled in the calculation of a B/C ratio relative to benefits, disbenefits, costs, or savings? The cost of grading and spreading gravel on a short rural road is expected to be $300,000. The road will have to be maintained at a cost of $25,000 per year. Even though the new road is not very smooth, it allows access to an area that previously could only be reached with off-road vehicles. The improved accessibility has led to a 150% increase in the property values along the road. If the previ- ous market value of a property was $900,000, calculate the B/C ratio using an interest rate of 6% per year and a 20-year study period. Arsenic enters drinking water supplies from natu- ral deposits in the earth or from agricultural and industrial practices. Since it has been linked to cancer of the bladder, kidney, and other internal organs, the EPA has lowered the arsenic standard for drinking water from 0.050 parts per million to 0.010 parts per million (10 parts per billion). The annual cost to public water utilities to meet the new standard is estimated to be $200 per house- hold. If it is estimated that there are 90 million households in the United States and that the lower standard can save 50 lives per year valued at $4,000,000 per life, what is the benefit/cost ratio of the regulation?Claudia works with Lockheed-Martin (LMCO) in the aircraft maintenance division. She is preparing for what she and her boss, the division chief, hope to be a new 10-year defense con- tract with the U.S. Air Force on C-5A cargo aircraft. A key piece of equipment for maintenance operations is an avionics circuit diagnostics system. The current system was purchased 7 years ago on an earlier contract. It has no capital recovery costs remaining, and the following are reliable estimates: current market value = $70,000, remaining life of 3 more years, no salvage value, and AOC = $30,000 per year. The only options for this system are to replace it now or retain it for the full 3 additional years. Claudia has found that there is only one good challenger system. Its cost estimates are: first cost = $750,000, life = 10 years, S = 0, and AOC = $50,000 per year. Realizing the importance of accurate defender alternative cost estimates, Claudia asked the division chief what system would be a logical follow-on to the current one 3 years hence, if LMCO wins the contract. The chief predicted LMCO would purchase the very system she had identified as the challenger, because it is the best on the market. The company would keep it for the entire 10 additional years for use on an extension of this contract or some other applica- tion that could recover the remaining 3 years of invested capital. Claudia interpreted the re- sponse to mean that the last 3 years would also be capital recovery years, but on some project other than this one. Claudia's estimate of the first cost of this same system 3 years from now is $900,000. Additionally, the $50,000 per year AOC is the best estimate at this time. The division chief mentioned any study had to be conducted using the interest rate of 10%, as mandated by the U.S. Office of Management and Budget (OMB). Perform a replacement study for the fixed contract period of 10 years.The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 30 mm and standard deviation 7.8 mm [suggested in the article "Reliability Evaluation of Corroding Pipelines Considering Multiple Failure Modes and Time- Dependent Internal Pressure" (,,1. of Infrastructure Systems, 2011: 216-224)]. a. What is the probability that defect length is at most 20 mm? Less than 20 mm? b. What is the 75th percentile of the defect length distribution-that is, the value that separates the smallest 75% of all lengths from the largest 25%? c. What is the 15th percentile of the defect length distribution? d. What values separate the middle 80% of the defect length distribution from the smallest 10% and the largest 10%?Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose that for banner-tailed kangaroo rats, X has an exponential distribution with parameter A = .01386(as suggested in the article "Competition and Dispersal from Multiple Nests," Ecology, 1997: 873-883) a. What is the probability that the distance is at most 100 m? At most 200 m? Between 100 and 200 m? b. What is the probability that distance exceeds the mean distance by more than 2 standard deviations? c. What is the value of the median distance?Construct a probability plot that will allow you to assess the plausibility of the lognormal distribution as a model for the rainfall data of Exercise 83 in Chapter 1. Reference exercise 83 Consider numerical observations X,.........X, . It is frequently of interest to know whether the xi s are (at least approximately) symmetrically distributed about some value. If n is at least moderately large, the extent of symmetry can be assessed from a stem-and-leaf display or histogram. However, if n is not very large, such pictures are not particularly informative. Consider the following alternative. Let y, denote the smallest x;, y2 the second smallest xi, and so on. Then plot the following pairs as points on a two-dimensional coordinate system: X1, . . . . *," There are n/2 points when n is even and (n-1)/2 when n is odd. a. What does this plot look like when there is perfect symmetry in the data? What does it look like when observations stretch out more above the median than below it (a long upper tail)? b. The accompanying data on rainfall (acre-feet) from 26 seeded clouds is taken from the article "A Bayesian Analysis of a Multiplicative Treatment Effect in Weather Modification" (Technometrics, 1975: 161-166). Construct the plot and comment on the extent of symmetry or nature of departure from symmetry.An alternative with an infinite life has a B/C ratio of 1.5. The alternative has benefits of $50,000 per year and annual maintenance costs of $10,000 per year. The first cost of the alternative at an interest rate of 10% per year is closest to: (a) $23,300 (b) $85.400 (c) $146,100 (ad) $233,000 Cost-effectiveness analysis (CEA) differs from cost-benefit (B/C) analysis in that: (a) CEA cannot handle multiple alternatives. (b) CEA expresses outcomes in natural units rather than in currency units. (c) CEA cannot handle independent alternatives. (d) CEA is more time-consuming and resource- intensive. Several private colleges claim to have programs that are very effective at teaching enrollees how to become entrepreneurs. Two programs, identi- fied as program X and program Y, have produced 4 and 6 persons per year, respectively, who were recognized as entrepreneurs. If the total cost of the programs is $25,000 and $33,000, respec- tively, the incremental cost-effectiveness ratio is closest to: (a) 6250 (b) 5500 (c) 4000 (d) 1333The joint probability distribution of the number X of cars and the number Y of buses per signal cycle at a proposed left-turn lane is displayed in the accompanying joint probability table. p(x, y) 0 2 .025 015 010 050 030 020 .125 .075 .050 UAWNEO .150 .090 060 .100 .060 040 .050 030 .020 a. What is the probability that there is exactly one car and exactly one bus during a cycle? b. What is the probability that there is at most one car and at most one bus during a cycle? c. What is the probability that there is exactly one car during a cycle? Exactly one bus? d. Suppose the left-turn lane is to have a capacity of five cars, and that one bus is equivalent to three cars. What is the probability of an overflow during a cycle? e. Are X and Y independent rv's? Explain