You would like to construct a 99% confidence interval to estimate the population mean score on a nationwide examination in psychology, and for this purpose we choose a random sample of exam scores. The sample we choose has a mean of 487 and a standard deviation of 74. (a) What is the best point estimate, based on the sample, to use for the population mean? (b) For each of the following sampling scenarios, determine which distribution should be used to calculate the critical value for the 99% confidence interval for the population mean. (In the table, Z refers to a standard normal distribution, and t refers to at distribution.) Could use Unclear Sampling scenario either Z ort The sample has size 17, and it is from a normally distributed population with an unknown standard deviation. The sample has size 100, and it is from a non-normally distributed population with a known standard deviation of 75. The sample has size 15, and it is from a population with a distribution about which we know very little.