1 Theory 1. In a. population with an average, a = 3, 000 and a variance, 02 = 36,000. Answer the following: (a) If you draw a random sample of 1,000 observations, what is the probability that the sample mean will be greater than 3,011.76 or less than 2,988.24? (b) If you draw a random sample of 4,000 observations, what is the probability that the sample mean will be greater than 2,995.065? (c) If you draw a random sample of 250 observations, what is the probability that the sample mean will be greater than 3,030.9