Discriminant analysis – credit scoring. A bank manager is trying to come up with an optimal decision rule for making short-term business loans based on credit scores. From past loans, the bank has two key types of clients: clients that have been defaulting have an average FICO score of 500; non-defaulters instead have a score of 800. Historically, the standard deviation of FICO scores is 100.
a. If the bank starts giving out loans to all customers with a score above 650, how often will the bank decline loan applications to non-defaulters ? How often will the bank grant application to defaulters? Assume the normal distribution.