You would like to construct a 90% confidence interval to estimate the population mean score on a nationwide examination in finance, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 513 and a standard deviation of 70. (a) What is the best point estimate, based on the sample, to use for the population mean? X ? D (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 90% 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 M Sampling scenario Z either Z or t Unclear The sample has size 105, and it is from a non-normally distributed X 3 ? O O O O population. The sample has size 20, and it is from a normally distributed population O O O O with a known standard deviation of 78. The sample has size 12, and it is from a normally distributed population O O O O with an unknown standard deviation