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- 1. f(x)= x - 3x4 - 6x3 + 10x2 + 21x + 9 +A water company owns water pipes that burst often due to poor maintenance. The company can invest GHS m in the maintenance of the pipes. More maintenance means less water loss through bursts and fewer compensation payments to residents due to flooding of their properties. Assume that the value of lost water is 1/m so that more maintenance reduces the amount of loss. Assume that the value of damage to properties where the pipes are routed is 3/m , so that more maintenance decreases the amount of damage to properties. (i.) What is the socially optimal level of maintenance, m? What is the associated value of lost water and property damage? (Note: Minimize the total cost function) ( ii). What level of m is chosen when pipes that burst run through land owned by the government (the company pays nothing for damages even though there is still some damage associated with pipe bursts)? What is the new value for property damage? What is the deadweight loss?Use the body temperatures, in degrees Fahrenheit, listed in the accompanying table. The range of the data is 3.3°F. Use the range rule of thumb to estimate the value of the standard deviation. Compare the result to the actual standard deviation of the data rounded to two decimal places, 0.69°F, assuming the goal is to approximate the standard deviation within 0.2°F. The estimated standard deviation is °F. (Round to two decimal places as needed.) Compare the result to the actual standard deviation. The estimated standard deviation is C the actual standard deviation. Thus, the estimated standard deviation Data table the goal. 99 98.2 97.5 98.4 99.2 98 98.7 98.5 98.1 98.1 98.5 99.3 98.7 96.7 96.5 98.7 98 97.3 98.4 98 97.7 98.3 98.9 97.1 99 97.1 98.7 98.6 99.4 97.6 97.6 97.7 97.9 99.4 98.7 99.6 97.8 97.9 99 98.3 97.7 98.7 98.2 98.7 97.6 98 97.7 98.6 98.5 98.3 97.7 99 96.3 98 98.2 96.8 97.3 97.3 97.5 98.5 97.6 97.7 97.2 97.7 98 98.8 99 98.5 98 97.8 97 97.3 99.1 98.7 98.6 98.3 98.4 99 98…
- Insurance: An insurance company sells a 1-year term life insurance policy to an 84-year-old man. The man pays a premium of $1600. If he dies within 1 year, the company will pay $33,000 to his beneficiary. According to the U.S. Centers for Disease Control and Prevention, the probability that an 84-year-old man will be alive 1 year later is 0.9537, Let X be the profit made by the insurance company. do Part: 0/2 Part 1 of 2 (a) Find the probability distribution. The probability distribution is 1600 P (x)To solve: A manufacturer of high-tech computing equipment must decide whether or not to continue development of a new promising technology. continuing the development would cost $2 Million. If the development is continued, then a patent is either awarded or not. 70% chance that the patent will be awarded and The best estimate is that there is a a 30% chance that it will not. if the patent is awarded, the company needs to decide whether or not to license the technology. it does, it would receive a total of $25 million in licensing royalties. However, the company could also produce and sell the technology in-house (at. a cost of $10 million), in which case there is an additional uncertainty about the demand for the technology. if the demand is high (p = 0.25), the company would make $55 Million in revenues, if the demand is medium (p = 0.55) the company would make $33 Million and if the demand is Low (p = 0.20) the company would still make $15 Million. a) Draw and solve a decision tree…Please see attachment and type out the correct answer ASAP with proper explanation of it.within 40 min. Will give you thumbs up only for the correct answer. Thank you
- 2. A city had an unemployment rate of 7%. The mayor pledged to lower this figure and supported programs to decrease unemployment. A group of citizens wanted to test with 0.032 label of significance if the unemployment rate had actually decreased, so they obtained a random sample of 500 citizens to see what proportion of the sample was unemployed. Only 32 citizens in the above sample is still unemployed. What is the probability of Type II error if the actual unemployment rate is 6.5% please don't use software everything needs to be done by hand. Explain because I don't understand my professor. Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.The number of major snowstorms (that shut down businesses) has a Poisson distribution with rate 0.4 per month Hom January through March. A restaurant buys an insurance policy to insure against losses. The policy pays nothing for the first major snowstorm that occurs in January through March, but pays $2,000 for every major snowstorm thereafter for that period up to $6.000. a) Find the probability there are 4 or more snow storms during the 3-month period. b) Find the expected amount paid by the policy during the 3-month period.Population of Fish in a Lake A lake is stocked with 100 fish. Let f(1) be the number of fish after i months, and suppose that y = f(1) satisfies the differential equation y' = .0004y(1000 – y). Figure 7 shows the graph of the solu- tion to this differential equation. The graph is asymptotic to the line y = 1000, the maximum number of fish that the lake can support. How fast is the fish population growing when it reaches one-half of its maximum population? 1000 800 600 400 200 10 15 Figure 7 Growth of a fish population.