1. Let X be normally distributed random variable with μ = 100 and σ = 10. Find the probability that X is between 75 and 100.
2. Let a random sample be taken of size n=36 from a population with known standard deviation of σ = 3. Suppose that the mean of the sample is x¯ = 37. The approximate 95% confidence interval for the mean, μ, of the population from which the sample was drawn. (Round the values to whole numbers for your confidence level.)