An insurance company offers two policies that cover the cost of repairs from driving accidents. A policy costing $1,000 annually has a $1,000 deductible (meaning the driver is responsible for paying the first $1,000 in damages before the insurance kicks in), whereas a policy that costs $3,000 annually has a $250 deductible. Assume that accidents that get reported to the insurance company require more than $1,000 to repair the car. If we model the number of accidents as a Poisson random variable with mean l, when is the policy with the $1,000 deductible cheaper for the driver on average?
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