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?