Suppose that the number of miles, X, until replacement is needed for a particular type of electric car battery follows an Exponential distribution with a mean of 200,000 miles. What is the probability...

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Extracted text: Suppose that the number of miles, X, until replacement is needed for a particular type of electric car battery follows an Exponential distribution with a mean of 200,000 miles. What is the probability that a randomly selected battery lasts at least 300,000 miles? 1. а. b. Suppose 10 batteries are chosen at random. What is the probability that exactly 4 of them last at least 300,000 miles? (Hint: You will need to define a new random variable.) С. The company that manufactures the battery comes up with a new and hopefully improved version that lasts Y miles until replacement. A random sample of 40 of these batteries are put in test cars that are driven extensively over a period of a couple of years until the batteries need to be replaced. The average number of miles until replacement is 320,000 with a standard deviation of 82,000. At an a = .05 level, do these data provide evidence that the true average time until replacement for these new batteries, u, is more than 300,000? Conduct a hypothesis test to determine your answer.