A sample of size n is drawn from a large population with mean μ and variance σ2 but unknown distribution;
(i) Determine the mean and variance of the sample mean when n = 10; μ = 50; σ2 = 20;
(ii) Determine the mean and variance of the sample mean when n = 20; μ = 50; σ2 = 20;
(iii) Determine the probability that a sample mean obtained from a sample of size n = 50 will not deviate from the population mean by more than ±3. State any assumption you may need to make in answering this question.