Applying the Central Limit Theorem
A nationwide study found that the average yearly claim per automobile insurance policy (after deductible) is $1,000 with a standard deviation of $400. Consider these parameter values to be the true population parameters. Suppose that you are working for a small, start-up insurance company with only 625 automobile insurance policies, and the company has $605,000 to pay for claims next year. What is the probability that the company will not have enough money set aside to pay off the claims next year? If the company does not have enough money set aside, it will declare bankruptcy and you will lose your job. Should you start working on your resume? Show your work and explain.