Claim Payment Probability 0 0.850 1000 0.050 2000 0.040 5000 0.030 25000 0.025 100000 0.004 500000 0.001

a.What is the expected claim payment made per customer in a year?

b.What is the probability that a randomly selected customer receives exactly the expected claim payment you calculated above in "a"?

c.What is the standard deviation of the claim payments made per customer in a year?

d.If the insurance company charges a $1850 premium to each customer, each year, then what amount does the insurance company make/lose per customer, each year? In a sentence or two, explain why the customers might be willing to pay the $1850 premium, given your calculations.

e.The critical value (or "z value") for statistical significance at the 10% level is 1.645 (remember?!). Thus, I'd like you to create a 90% confidence interval by taking:

Expected Claim Payment + 1.645(standard deviation of claim payment)

Now that I have this interval, I know that a randomly selected insurance customer will have a 90% chance of receiving claim payments within this confidence interval.

Do you agree with the above, italicized, analysis? In a sentence, explain why or why not.