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...

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?