Expexcted value

Question

An insurance company charges 1350 annually for insurance premiums. Each time a patient is hospitalized it costs the hostpital 2500. They estimated that 81% of patients will not be hospitalized and 11% will be hospitalized once a year. No one wil be more than twice. Find the company's expected profit per policy holder. Then find the expected profit of they enroll 80,000 policy holders.

Answer 1

Let x be the number of people who use the insurance company.  If 81% never go to the hospital and 11% go once, then that leaves 8% who go twice.

 

1350x - 2500(.11x) - 2500*2(.08x)

1350x - 275x - 400x

675x

 

So they make $675 per person who signs up, and you now have the profit function to figure out exactly how much profit they'd expect to make for 80,000 holders.