The Real Estate Bank Limited (REBL) is a financial institution specializing in residential real estate investments. The company has been approached by a small community bank offering mortgage backed securities for sale. The securities valued at $100 million are backed by a pool of mortgages of equivalent value. The standard deviation of the assets in the pool is 5% and management expects the mortgage to default if the value of the assets falls below $90 million. The Trust is unwilling to invest in any debt instrument with a probability of default greater than 2.25%. You are approached by management to determine the probability of default and recommend whether this purchase should be made. Prepare a brief response to management (show your calculations and assumptions).