Question

A customer buys a $250,000 life insurance policy with an annual premium of $300. Her probability of dying during the year is 0.001. If she dies, the insurance company will have to give her beneficiary $250,000. a) If there is a 0.001 chance she dies, what is the probability she does not die? b) Fill in the table below, let X= Amount the insurance company makes. X P(X) c) Use a computer or calculator: What is the insurance company’s expected value for this policy? With what standard deviation? Write a sentence that shows you understand what an expected value is.

Answer 1

a)

Given that :

P(die) = 0.001

The probability she does not die is

1- P(die) = 1 - 0.001 = 0.999

b)

If person die insurance company need to pay 250000 -300 = 249700.

If person survive insurance company get 300.

Following is completed table:

X	P(X=x)
-249700	0.001
300	0.999

Following table shows the calculations for mean and SD:

X	P(X=x)	xP(X=x)	x^2*P(X=x)
-249700	0.001	-249.7	62350090
300	0.999	299.7	89910
Total		50	62440000

The expected value for insurance company is

The standard deviation for insurance company is