A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a .96 probability of functioning, and twohave a probability of .99. What is the overall probability that the product will function properly?
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A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a .96 probability of functioning, and two
have a probability of .99. What is the overall probability that the product will function properly?
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- A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a 0.96 probability of functioning, and two have a probability of 0.99. (Leave your answers in 4 decimal places).Hoping to increase the chances of reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 9, 8, and 7 for successfully completing the task in the allotted time Assuming that the teams work independently, what is the probability that the task will not be completed in time?A company installs new central-heating furnaces and has found that for 15% of all installations, a return visit is needed to make some modifications. Six installations were made in a particular week. Assume independence of outcomes for these installations.a. What is the probability that a return visit will be needed in all these cases?b. What is the probability that a return visit will be needed in none of these cases?c. What is the probability that a return visit will be needed in more than 1 of these cases?
- 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.If the probability of a defective light bulb is 0.07, to be 90 % confident, up to how many defective lightbulbs should you expect in a sample of 39 lightbulbs? F-1(0.9)= (Specify your answer as a whole number.)In designing a new space vehicle, NASA needs to decide whether to provide 0, 1 or 2 backup systems for a critical component of the vehicle. The first backup system, if included, comes into use only if the original system fails. The second backup system, if included, comes into use only if the original system and the first backup system both fail. NASA engineers claim that each system, independent of the others, has a 1.5% chance of failing if called into use. Each backup system costs $70,000 to produce and install within the vehicle. Once the vehicle is in flight, the mission will be scrubbed (ended early) only if the original system and all backups fail. The cost of a scrubbed mission, in addition to production costs, is assessed to be $5,000,000. How many backup systems are needed to minimize NASA’s expected total cost?
- A company is considering whether to develop and market a particular product. There is 40% probability that the research and development department will come up with a viable product, and a 60% probability that the product will be scrapped. The cost of undertaking the research and development is 200 000.By means of extensive testing, a manufacturer has determined that its Super Sucker Vacuum Cleaner models have an expected life that is exponential with a mean of four years.Find the probability that one of these cleaners will have a life that endsa. After the initial four years of service.A major television manufacturer has determined that its 40-inch LED televisions have a meanservice life that can be modeled by a normal distribution with a mean of six years and a standarddeviation of one-half year.a. What probability can you assign to service lives of at least (1) five years? (2) six years? (3)seven and one-half years?
- 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?At DataTech Solutions, the reliability of their server systems is a critical factor in maintaining smooth operations. The company knows that the probability of a server experiencing no downtime due to technical issues is 0.95. When a server is functioning smoothly, there is a 0.9 probability that the network performance is also optimal. However, if a server encounters technical problems, the probability of having optimal network performance drops to 0.3. A server is chosen at random for assessment, and its network performance is found to be optimal. What is the updated probability that the server is running without any technical issues?Scenario: Imagine you are a physician who has been whose patient has the following matter up to you. The patient has an unusual infection, which lasts for a short time. The infection has a 15% chance of causing permanent brain damage. You may undertake a procedure that will prevent the brain damage from the infection (with 100% probability). However, the procedure itself has a 20% chance of causing brain damage itself. Should you undertake the procedure or not? Question: Identify whether the scenario poses a problem to solve or a decision to be made. Explain HOW and WHY you came to your answer?