Question: Let X be a (population) random variable with a mean Question 4 Let X be a (population) random variable with a mean a and variance

Let X be a (population) random variable with a mean

Question 4 Let X be a (population) random variable with a mean a\" and variance 0'2. Consider a random sample OfXI X13X21n-gX-n- What is the distribution ofthe sample mean f\" = X1 + X2 :1- + X\" when n is sufciently large? Now suppose that n. is sufciently large, and o2 = ng. What is the probability that the sample mean in is between 0.9a and 1-1:\" when n. = 36? What is the probability that the sample mean in is between 0.9,u and 1.1;; when n. = 49? What is the probability that the sample mean f\" is between 0.95,\" and 1.05;; when n. = 49"? What is the probability that the sample mean f\" is between 0.95pm and 1.05\" when n. = 64? (Again, use the normal table.)

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