. The failure of power transformers is assumed to follow Poisson probability distribution. Suppose on average, a transformer fails once every 5 years. What is the probability that it will fail once in the next 24 months? * 0.3681 0.2681 0.4681 0.1681
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- kindly help me with this problem in JOINT PROBABILITY DISTRIBUTION follow this formath Given; Required; & Solution thank you!The useful life of Johnson rods for use in a particular vehicle follows an exponential distribution with an average useful life of 5.2 years.You have a three-year warranty on your vehicle’s Johnson rod. What is the probability that the Johnson rod doesn’t fail before then? That is, what is the probability that its useful life doesn’t end before three years?b.If the vehicle manufacturer wants to limit the number of claims on the three-year warranty to 20%, what should the average useful life of the Johnson rod be?A sample of a radioactive material is studied in a lab. There are 741 gamma ray emissions over 130 seconds. Use the Poisson distribution to find the probability that 1 or fewer gamma rays are emitted in a given second. Do not round intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.) ?
- The principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 14.9% daily failure rate. Complete parts (a) through (d) below. a. What is the probability that the student's alarm clock will not work on the morning of an important final exam? (Round to three decimal places as needed.)A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. What is the arrival rate? (Include the units.) What is the service rate? (Include the units.) Find the probability that the employee is idle.Please answer this ASAP with complete solution
- indicate the units to the final answer if any Draw the necessary graph if any. Round off to four decimal places or in lowest term if your answer is in fraction.Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…local gym has only one treadmill machine for cardio exercises. Suppose exponential interarrival times with mean of 2 per hour, and exponential usage times with mean of 30 minutes per customer. Suppose a person has just arrived at 12.00 noon to use Assume your the machine. What is the probability that the next arrival will come before 1.00 pm, between and after 2.00 pm? Note that you have to provide three 1.00 pm and 2.00 pm, answers, one for each. Suppose no customer arrives before 1.00 pm. What is the probability that the next arrival will come between 1.00 pm and 2.00 pm? What is the probability that the number of arrivals between 1.00 pm and 2.00 pm will be zero (one, more than one)?