5. A health insurance company charges policyholders a $2250 annual premium for h

Question

5. A health insurance company charges policyholders a $2250 annual premium for health insurance for hospitalization. The company estimates that each time a patient is hospitalized costs the company $2900. Furthermore, they have estimated that 85% ofpatients will not be hospitalized, 10% will be hospitalized once a year, and no one will be hospitalized more than twice. (a) Find the insurance company's expected profit per policyholder. (b) What is the expected profit if they enroll 80,000 policyholders?

Explanation / Answer

a) expected profit per policyholder =premium paid -expected cost of hospitalization for once a year -expected cost of hospitalization for twice a year

=2250-2900*0.1-2900*2*0.05=1670

b) expected profit from 80000 policyholders =80000*1670=133600000

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