An insurance company has a life insurance policy, which have 10,000 clients, each client pays 200 yuan per year. If the client died in this year, the company paid out the beneficiary of 10,000 yuan. The mortality rate for the client is 0.017 , and what is the probability of the insurance company will deficit in this year?
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An insurance company has a life insurance policy, which have 10,000 clients, each client pays 200 yuan per year. If the client died in this year, the company paid out the beneficiary of 10,000 yuan. The mortality rate for the client is 0.017 , and what is the probability of the insurance company will deficit in this year?
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- A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000 Construct a decision tree to help the farmer make his decision. What should he do? Explain your answer. Find the highest cost of insulating the grapefruits for which the farmer prefers to insulate his crop. Suppose the farmer is uncertain about the reliability of the National Weather Service forecast. If he thinks the probability of…A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000 a. Construct a decision tree to help the farmer make his decision. What should he do? b. Find the highest cost of insulating the grapefruits for which the farmer prefers to insulate his crop. c. Suppose the farmer is uncertain about the reliability of the National Weather Service forecast. If he thinks the probability of a freeze occurring…A farmer must decide whether to take protective action to limit damage to his grapefruit crop in the event that the overnight temperature falls to a level well below freezing. If the temperature drops too low he runs the risk of losing his entire crop, valued at $75,000. Based on the National Weather Service, the probability of such a temperature drop is 60%. He can insulate his crop by spraying water on all the trees, which will cost $20,000. This action might succeed in protecting the crop, with the following possible outcomes: Probability Damage 0.30 $0 0.15 $5,000 0.10 $10,000 0.15 $15,000 0.30 $20,000 Construct a decision tree to help the farmer make his decision. What should he do?
- A car repair can be performed either on time or late, and either satisfactoryily or unsatisfactorily. The probability of a repair being on time and satisfactory is 0.26. The probability of a repair being on time is 0.74. The probability of a repair being satisfactory is 0.41. What is the probabilityof a repair being late and unsatisfactory?A project will cost $45,000 to develop.• When the system becomes operational after a one-year development period, operational costs willbe $9,000 during each year of the system’s five-year useful life.• The system will produce benefits of $30,000 in the first year of operation, and this figure willincrease by a compound 10% each year.What is the payback period for this project?4. From past experience, Anna knows that the probability that her friend will take her to dinner in Orro Resto id 0.7, the probability that they will watch movies is 0.5, and the probability that he will take her to dinner or they will watch movies is 0.9. What is the probability that they will do both? they will do neither? 5. Eight persons enter a supermarket. From the past experience, it is known that 25% of the people entering the supermarket make a purchase. What is the possible values of the random variable X? Construct the probability distribution of X. X P(X=x) What is the probability that 1) at least four persons will make a purchase? 2) two or three persons will make a purchase? 3) a most two persons will make a purchase?
- An expensive piece of equipment is used in the masking operation for semiconductor manufacture.A capacitor in the equipment fails randomly. The capacitor costs $7.50, but if it burns out while the machine is in use, the production process must be halted. Here the replacement cost is estimated to be $150. Based on past experience, the lifetime distribution of the capacitor is estimated to be Number of Months Probability of of Service Failure 1 .08 2 .12 3 .16 4 .26 5 .22 6…Embassy Publishing Company received a six-chapter manuscript for a new college textbook. The editor of the college division is familiar with the manuscript and estimated a 0.7207 probability that the textbook will be successful. If successful, a profit of $850,000 will be realized. If the company decides to publish the textbook and it is unsuccessful, a loss of $150,000 will occur. Before making the decision to accept or reject the manuscript, the editor is considering sending the manuscript out for review. A review process provides either a favorable (F) or an unfavorable (U) evaluation of the manuscript. Past experience with the review process suggests probabilities P(F) = 0.7 and P(U) = 0.3 apply. Let s1 = the textbook is successful, and s2 = the textbook is unsuccessful. The editor's initial probabilities of s1 and s2 will be revised based on whether the review is favorable or unfavorable. The revised probabilities are as follows: P(s1|F) = 0.85 P(s2|F) = 0.15…The number of hybrid cars that have be requested for rental from a car rental office during a 50 day sample period is given in the following table. Demand for Cars Number of Days Probability 3 3 0.06 4 7 0.14 5 12 0.24 6 14 0.28 7 10 0.20 8 4 0.08 50 1.00What is the expected (mean) number of hybrid rentals per day? Compute to one decimal place.
- A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost $85,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only $70,000 to install. However, the vinyl is not guaranteed to last for all 10 years, and it has a 40% chance of breaking down. Repair of the vinyl would cost $40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes cost? Support your answer with drawing a decision tree and provide your calculation.The Hoylake Rescue Squad receives an emergency call every 1, 2, 3, 4, 5, or 6 hours, accordingto the following probability distribution. The squad is on duty 24 hours per day, 7 daysper week:Time BetweenEmergency Calls (hr.) Probability1 .052 .103 .304 .305 .206 .051.00 Compute the average time between calls and compare this value with the expected value of the time between calls from the probability distribution. Why are the results different?Automobile repair cost continue to rise with the average cost now at $367 per repair. Assume that the cost for an automobile repair is normally distributed with a standard deviation of $88. A) what is the probability that the cost will be more than $480? B) what is the probability that the cost will be less than $290? C) what if the probability that the cost will be between $290 and $480? D) if the cost for you car repair is in the lower 5% of automobile charges, what is your maximum possible cost in dollars?