1. Given a population with mean 50 and standard deviation of 6. a) State the sampling distribution of the mean for a sample size of n = 15 b) Find the probability that the mean will be between 40 and 60 for this sample. c) State the sampling distribution of the mean for a sample size of n = 20 d) Find the probability that the mean will be between 40 and 60 for this sample. 2. Suppose we are given a population known to be normally distributed with standard deviation a = 2.8, but the population mean, , is unknown. The following sample of nine: 8, 9, 10, 13, 14, 16, 17, 20, 21, comes from this population. Use this information to compute a) The 95% confidence interval. b) The 99% confidence interval. c) Which interval is wider? Explain why