44. A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77 (AAII Journal, February 2006). The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.

a. Using the sample data, what is the margin of error associated with a 95% confidence interval?

b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share.