8-7. Suppose a population variable X is N(2800, 2500). If a random sample of size n = 36 is selected, find the probability that the sample mean X will not differ from the population mean μ by more than 30. Within what interval would X fall 90% of the time under random sampling for samples of size 36? How large of a sample must be taken so that the probability that X is within 20 units of μ is 0.95?