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Question 2 [Avec R] Say you can ask people to give a rating of a potential product. The population mean of this products rating is μ, which is unknown. If you ask a single person. they will respond with a random variable that has a mean μ and a variance of 100. (a). Call n the number of people sampled and x =-Σ-1x, the sample mean of each individuals response. This will be your cstimate. What is the approximate distribution of x-μ using the central limit theorem? (b). Your boss gives you the authority to sample some number of people. Sampling more people is more expensive. He says be mindful of the budget, but he wants your estimate to differ from 11 by less than 1 with probability at least 0.95. What is the smallest sample size can you choose to meet this criteria?

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