Suppose that a bank uses an applicant's score on some criteria to decide whether or not to approve a loan for the applicant. Suppose for now that these scores follow normal distributions, both for people who would repay to the loan and for those who would not. Those who would repay the loan have a mean of 70 and standard deviation of 8; those who would not repay the loan have a mean of 30 and standard deviation of 8.

The left one is the distribution for those who would not repay the loan and the right one is the distribution for those who would repay the loan.

Question (1) Suggest a decision rule, based on using an applicant's score, for deciding whether or not to give a loan to the applicant. Describe the two kinds of classification errors that could be made in this situation.

Question (2) Determine the probabilities of the two kinds of error with this rule. Write a sentence or two to interpret the two error probabilities in context.

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