An automobile insurance company wishes to estimate the total cost of settling insurance claims.It estimates it will need to service 2 million claims next year.They take a random sample of 3,000 cases from the past three years.They find that the average initial claim is $1,500, the standard deviation is $800, and the numbers are approximately Normally distributed.

a)How many initial claims can they expect to be over $2,500?Hint:Draw picture, use the Z table, or Excel.

b)What number will 95% of the initial claims be less than?

c)What would you estimate the total cost of settling claims will be?

d)Give two arguments for why the distribution is not going to be Normal.The first argument should be based on the numbers in the problem.The second argument should be based on why you believe the distribution will be skewed and possibly "bimodal".

e)How does your answer to question d affect your faith in your answer to questions a & b?