Question

There is a 0.9968 probability that a female lives through the year. The cost of one year premium is $226. If she dies within the year the policy pays %50,000 in death benefit.

A. State the two events representing possible outcomes

B. Calculate the female's expected gain

450 policies are sold in one year. Let x = # of policyholders who die within the year.

C. Calculate the company's total intake from premiums for one year.

D. If the company is to make a profit, state the possible value(s) of x.

E. Find the probability that company makes a profit.

*Please show work, thank you*

Answer 1

Given robability that a female lives through the year is 0.9968 .

A) the two events are

1) The female lives in the year with probability 0.9968 and pays $226 premium.

2) The female dies in the year with probability 1-0.9968 = 0.0032 , pays $226 premium and gets $50,000.

B) The female's expected gain is

There is a loss for the female. Gain for the company (that is how the company survives, otherwise they will not do this business).

C) Given 450 policies are sold in one year. Let of policyholders who die within the year.

The company's total intake from premiums for one year is

D) The net gain of the company is

When the company makes a profit,

So the possible values of  .

E) The probability that females die in year is (Use binomial distribution).

The number of females out of 450 who dies in year has PMF

The PMF of is  

The probability that company makes a profit is