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Jasovan Insurance Company insures 100,000 drivers who have each been driving for at least five years. Each driver gets violations at a Poisson rate

 

Jasovan Insurance Company insures 100,000 drivers who have each been driving for at least five years. Each driver gets "violations" at a Poisson rate of 0.5/ year. Currently, drivers with 1 or more violations in the past two years pay a premium of 1,200. Drivers with 0 violations in the past two years pay 650. The marketing department wants to change the pricing so that drivers with 2 or more violations in the past five years pay 1,300 and drivers with zero or one violations in the past five years pay X. Find X so that the total premium revenue for the firm has an increase of 5% from the previous amount when this change is made.

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