Question

Suppose that an insurance company insures more than one million individuals with a policy that the company actuaries believe will net them an average profit of $20$20 per month per policy (total premiums collected minus payouts for claims and overhead, divided by the number of such policies that they carry). Assume that total dollar amount of claims each month varies randomly.

Which of the statements do not accurately reflect the meaning of the law of large numbers.

1.In one particular month, the policies resulted in a profit of $30$30 per policy. Therefore, the next month is likely to show a net loss of $10$10 per policy.

2.As more months go by, the average profit per policy gets closer to $20.$20.

3.The company will show a profit of $20$20 per policy every single month.

4.In one particular month, the policies resulted in a net loss of $15$15 per policy. Therefore, the next month is likely to show a net profit of $35$35 per policy.

5.In one particular month, the policies resulted in a net profit of $50$50 per policy. Therefore, the company must have been selling the policies for a very large number of months.

Answer 1

The following are the statements that do not accurately reflect the meaning of the law of large numbers

• In one particular month, the policies resulted in a profit of $30 per policy. Therefore, the next month is likely to show a net loss of $10 per policy
• In one particular month, the policies resulted in a profit of $50 per policy. Therefore, the company must have been selling the policies for a very large number of months
• The company will show a profit of $20 per policy every single month
• In one particular month, the policies resulted in a loss of $15 per policy. Therefore, the next month is likely to show a net profit of $35 per policy

P.S: Only the second statement accurately reflect the meaning of the law of large numbers.

As more months go by, the average profit per policy gets closer to $20.

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