Like other businesses, insurance companies seek to minimize expenses associated with doing business to enhance profitability. To study expenses, this exercise examines a random sample of 500 insurance companies from the National Association of Insurance Commissioners’(

NAIC) database of more than 3,000 companies. The NAIC maintains one of the world’s largest insurance regulatory databases; we consider here data that are based on 2005 annual reports for all the property and casualty insurance companies in the United States. The annual reports are financial statements that use statutory accounting principles.

Specifically, our dependent variable is EXPENSES, the nonclaim expenses for a company. Although not needed for this exercise, nonclaim expenses are based on three components: unallocated loss adjustment, underwriting, and investment expenses. The unallocated loss adjustment expense is the expense not directly attributable to a claim but indirectly associated with settling claims; it includes items such as the salaries of claims adjusters, legal fees, court costs, expert witnesses, and investigation costs. Underwriting expenses consist of policy acquisition costs, such as commissions, as well as the portion of administrative, general, and other expenses attributable to underwriting operations. Investment expense are those expenses related to investment activities of the insurer.

a. Examine the distribution of the dependent variable, EXPENSES. Do this by making a histogram and then a qq plot, comparing the empirical to a normal distribution.

b. Take a natural log transformation and examine the distribution of this transformed variable. Has the transformation helped to symmetrize the distribution?