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# Borrower Characteristics

1. In examining borrower characteristics versus loan delinquency, a bank has collected the following information. 15% of borrowers who have been employed at their present job for less than 3 years are behind in their payments, 5% of the borrowers who have been employed at their present job for at least 3 years are behind in their payments, and 80% of the borrowers have been employed at their present job for at least 3 years.

a. What proportion of borrowers are behind in their payments?

b. You randomly select one loan account. What is the probability the borrower has been in the same job for at least three years and is behind in their payments?

c. You randomly select one loan account and note that the borrower is behind in their payments. What is the probability the borrower has been in the same job for less than three years?

d. Are the events employed in present job at least three years and behind in their payments independent?

2. It has been reported that the overall graduation rate for football players at Division I-A colleges and universities is 65%. You take a random sample of five players from the entire population of Division I-A football players.

a. What is the probability that exactly two of the five players sampled will graduate?

b. What is the probability that at least four of the five players sampled will graduate?

c. What is the expected number of players in the sample of 5 who will graduate?

3. The precooked weight of hamburgers at a gourmet hamburger restaurant has been normally distributed with a mean of 5.5 ounces and a standard deviation of 0.15 ounces. A dining-column journalist from the local newspaper enters the restaurant and orders a hamburger.

a. What is the probability that he will receive a hamburger that had a precooked
weight greater than 5.75 ounces?

b. What is the probability that he will receive a hamburger that had a precooked
weight between 5.6 and 5.7 ounces?

c. What precooked weight is exceeded by 10 percent of the hamburgers?

#### Solution Preview

Please see the attached file for the full solution.

1. In examining borrower characteristics versus loan delinquency, a bank has collected the following information. 15% of borrowers who have been employed at their present job for less than 3 years are behind in their payments, 5% of the borrowers who have been employed at their present job for at least 3 years are behind in their payments, and 80% of the borrowers have been employed at their present job for at least 3 years.

a. What proportion of borrowers are behind in their payments?
Solution. Let A be the event : the employed in present job at least three years
B be the event: behind in their payments
Given , , . So,

b. You randomly select one loan account. What is the probability the borrower has been in the same job for at least three years and is behind in their payments?
Solution.
...

#### Solution Summary

The solution looks at borrower characteristics including football player graduation rate and burger weights.

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