Problem 4: The idea of insurance is that we all face risks that are unlikely but carry high cost. Workers' compensation insurance provides for the cost of medical care, rehabilitation, and other
related expenses for injured workers. In a given year, most workers will not have any work
injury, some will have minor injuries, and a few will die or become permanently disabled.
Insurance spreads the risk: We all pay a small amount, and the insurance policy pays a large
amount to these few extreme claims. The National Academy of Social Insurance reports that the
mean workers' compensation claim cost in a year is u = $439 per insured worker, and the
standard deviation is o = $20,000. The distribution of losses is strongly right-skewed: Most
policies have no loss, but a few have large losses, up to millions of dollars.
a) An insurance company plans to sell workers' compensation insurance for S439 plus
enough to cover its administrative costs and profits. Explain clearly why it would be
unwise to sell only 12 polices. Then explain why selling thousands of such policies is a
safe business.