Question #1: In July 2010, Lender Processing Service 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 sampling distribution model for the sample proportion of foreclosures? Check the conditions and discuss any assumption you need to make. B. Sketch and clearly label the sampling model, based on the 68-95-99.7 Rule. C. How many of these homeowners might the bank expect will default on their mortgages? Explain.

Question #2: The weight of potato chips in a medium size bag is stated to be 10 ounces. The amount that the packaging machine puts in these bags is believed to have a Normal model with mean 10.2 ounces and standard deviation 0.12 ounces.

A. What fraction of all bags sold are underweight?

B. Some of the chips are sold in “bargain packs” of 3 bag. What’s the probability that none of the 3 is underweight?

C. What’s the probability that the mean weight of the 3 bags is below the stated amount?

D. What’s the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces?

**Subject Mathematics Advanced Statistics**