Question

QUESTION 9 (Adapted from Statisties for Management and Econormics.9th edition by Gerald Keller) Credit scores are used by fnancial institutions to them make decisions about to whom to grant a loan request. Many factors aflect a person's score, but one of the most important is whether a person pays his or her debts back in a timely manner The higher the score, the more likely the person is to pay his or her debts on time, or so the theory goes. An analysis of records at a large financial institution produced the following counts related to payment behavior and credit score. Before working the problem, turn these data into probabilities by dividing each number in the table by the total number of observations What is the probablity that, given a person has a score of 400 or more, he or she will fully repay a loan? Report your answer to three decimal places Score <400 400 or Behavior Re 56 1489 500 385 Defaulted

Answer 1

Total number of loans = 1830

	<400	400 or more
Fully Repaid	0.249	0.267
Defaulted	0.273	0.210

P(fully repaid | score of 400 or more) = P(fully repaid and 400 or more)/P(400 or more)

= 0.267/(0.267+0.210)

= 0.560

OR

P(fully repaid | score of 400 or more) = 489/(489+385)

= 0.559