Net interest margin-often referred to as spread-is the difference between the rate banks pay on deposits and the rate they charge for loans. Suppose that the net interest margins for all U.S. banks are normally distributed with a mean of 4.15 percent and a standard deviation of .5 percent.
a. Find the probability that a randomly selected U.S. bank will have a net interest margin that exceeds 5.40 percent.
b. Find the probability that a randomly selected U.S. bank will have a net interest margin less than 4.40 percent.
c. A bank wants its net interest margin to be less than the net interest margins of 95 percent of all U.S. banks. Where should the bank's net interest margin be set?