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1. CNNBC recently reported that the mean annual cost of auto insuranceis 960 dollars. Assume the standard deviation is 209 dollars. You take a simple random sample of 57 auto insurance policies.Find the probability that a single randomly selected value is at least 961 dollars.P(X > 961) =Find the probability that a sample of size n=57 is randomly selected with a mean that is at least 961 dollars.P(M > 961) =Enter your answers as numbers accurate to 4 decimal places.2. A leading magazine (like Barron’s) reported at one time that the average number of weeks an individual is unemployed is 23 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 23 weeks and that the population standard deviation is 2.4 weeks. Suppose you would like to select a random sample of 53 unemployed individuals for a follow-up study.Find the probability that a single randomly selected value is greater than 23.6.P(X > 23.6) = (Enter your answers as numbers accurate to 4 decimal places.)Find the probability that a sample of size n=53 is randomly selected with a mean greater than 23.6.P(M > 23.6) = (Enter your answers as numbers accurate to 4 decimal places.)MathStatistics and Probability STATISTICS 5301

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