B. Ciochetti et al. studied mortgage loans in the article "A Proportional Hazards Model of Commercial Mortgage Default with Originator Bias" (Journal of Real Estate and Economics, Vol. 27, No. 1, pp. 5-23). According to the article, the loan amounts of loans originated by a large insurancecompany lender have a mean of $6.74 million with a standard deviation of $15.37 million. The variable "loan amount" is known to have a right-skewed distribution.
a. Using units of millions of dollars, determine the sampling distribution of the sample mean for samples of size 200. Interpret your result.
b. Repeat part (a) for samples of size 600.
c. Why can you still answer parts (a) and (b) when the distribution of loan amounts is not normal, but rather right skewed?
d. What is the probability that the sampling error made in estimating the population mean loan amount by the mean loan amount of a simple random sample of 200 loans will be at most $1 million?
e. Repeat part (d) for samples of size 600.