Question

Diagrams of the normal distribution are almost mandatory

A health insurance company charges policyholders a $2450 annual premium for health insurance for hospitalization. The company estimates that each time a patient is hospitalized costs the company $3600. Furthermore, they have estimated that 85% of patients 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 90,000 policyholders?

Answer 1

a)

X : insurance company's net gain amount and P( x) is Corresponding probability.

If patient is not hospitalized then company's gain is $2450 with probability 0.85

If patient is hospitalized once a year then company's gain is -$1150 with probability 0.10

If patient is hospitalized twice a year then company's gain is -$4750 with probability 0.05

So expected profit of insurance company per customer is

E(X) = X*P(X)

= 2450*0.85 -1150*0.10 - 4750*0.05

E( X) = $ 1730

b) if 90000 policy holder enrolled then expected profit

Expected profit = N*E(x)

Expected profit = 90000*1730

Expected profit = 155,700000