You would like to construct a 95% confidence interval to estimate the population mean annual income for people over age 40 in your state. You choose a random sample of such incomes and compute the mean of the sample as 40,681.5 dollars with a standard deviation of 7734.2 dollars. (a) What is the best point estimate, based on the sample, to use for the population mean? X 5 dollars (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 95% confidence interval for the population mean. (In the table, Z refers to a standard normal distribution, and t refers to a t distribution.) Could use Sampling scenario Z t Unclear either Z or t The sample has size 12, and it is from a normally distributed X 5 O O O O population with an unknown standard deviation. The sample has size 105, and it is from a non-normally distributed O O O O population. The sample has size 95, and it is from a non-normally distributed O O O O population with a known standard deviation of 7482