4. (3 points) In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 38 recent loans is taken. The average calculated from this sample is 3.19%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.50%. a. Compute the margin of error at a 95% confidence interval. b. Compute a 95% confidence interval for the population mean 30-year fixed mortgage rate. c. Compute a 90% confidence interval for the population mean 30-year fixed mortgage rate