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In: Statistics and Probability

Bird’s data analyst wants to model the sample mean and sample variance of net revenue of...

Bird’s data analyst wants to model the sample mean and sample variance of net revenue of scooters. They plan to take a random sample of 25 of its scooters in Austin. They will record weekly net revenue brought in by each scooter. They decide it is reasonable to assume that weekly revenue of scooters is approximately normally distributed with a standard deviation of $50 (variance of 2,500 squared dollars).
Find values a and b such that (i) the probability is 0.9 that the sample standard deviation s will be between a and b and (ii) the probability is 0.05 that s will be less than a. What is the value of a? what is the value for b?

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