Question: 47: Net interest margin – referred 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% and a standard deviation of 0.5%.

(a) Find the probability that a randomly selected bank will have a net interest margin less than 5.4%

(b) Find the probability that a randomly selected bank will have a net interest margin less than 4.4%

(c) A bank wants its net interest margin to be less than the net interest margin of 95% of all U.S. banks. Where should the bank’s net margin be set?