An insurance company sells homeowner's insurance policies in a certain area. The company has collected data on the average number of claims per year, the average amount paid per claim, and the standard deviation of the amount paid per claim. Based on this data, the company has calculated the expected value of the annual claim cost to be $10,000, with a standard deviation of $2,000.

a) What is the probability that the annual claim cost will be less than $8,000?

b) If the company wants to have a 95% confidence level that its total claims paid in a year will not exceed $1 million, what is the maximum number of policies it can sell?

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