In July 2012 Lender Processing Services reported that homeow

In July 2012, Lender Processing Services reported that homeowners were defaulting in record numbers; 12.4% of mortgages were delinquent or in foreclosure. Suppose a large bank holds 1731 adjustable-rate mortgages.

a) Can you apply the Central Limit Theorem to describe the sample proportion of forclosure? Check the conditions and discuss any assumptions you need to make.

b) sketch and clearly label the sampling model based on 68-95-99.7 rule

c) How many of these homeowners might the bank expect will default on their mortgages? Explain.

Solution

Central limit theorem can be applied if sample size >30 and no outlier is there.

Hence we can apply

b)

c) Expected value of defaulters =np

= 1731(12.4%)

= 214.644