3.An automobile insurance provider has a portfolio of 3,000 policies. In any given year, the expected number of claims is 50. The CFO states that a material consequence to company would be claims numbering 75 or more in a given year. The annualized probability of a claim for any one policy is 2%.

a) What is the annual probability of having less than 50 claims?

b) What is the annual probability of having 75 or more claims (the tipping point of a material consequence)?

c) Given the tipping point has occurred, what is the 10th, 50th, and 90th percentile number of claims in a given year?