Suppose that you have analyzed thousands of approved loan applications and whether the loans were paid in full or resulted in default. You have developed a model that uses the application data to predict whether the loan would result in default or full payment. The model has been applied to a hold out sample of $2,000$ loans to see how it would perform in practice. The results are summarized in the confusion matrix below. In this setting, we consider a "positive" outcome to be paid in full.

$\backslash$table$[[$Prediction $\backslash$Truth$,$Paid,Default,Total$],[$Paid$,1,763,43,1,806],[$Default$,85,109,194],[$Total$,1,848,152,2,000]]$

a$.$ What is the accuracy rate for this model? Explain the meaning of "accuracy rate" in words that a bank manager would understand.

b$.$ What is the "sensitivity rate" for the model? Explain the meaning of this "sensitivity rate" in words the bank manager would understand.

c$.$ What is the "specificity rate" for the model? Explain the meaning of this "specificity rate" in words the bank manager would understand.

d$.$ What is the "false omission rate" for the model? Explain the meaning of this "false omission rate" in words the bank manager would understand.

e$.$ What is the "fiplse detection rate" for the model? Explain the meaning of this "false detection rate" in words the bank manager would understand.

f$.$ Before the model was created, the bank had been approving all of these loans, so it had predicted that they would all be paid in full. What was the accuracy rate for the bank's predictions?

g$.$ Suppose that loans that are paid off result in an average profit of $$900,$ but loans that end in default result in an average loss of $$600.$ On this basis, would the model generate more profit that the bank's current practice for these $2,000$ applications? If not, why not?