Question

Suppose a life insurance company sells a ​$260 comma 000260,000 ​one-year term life insurance policy to a 2424​-year-old female for ​$350350. The probability that the female survives the year is 0.9996410.999641. Compute and interpret the expected value of this policy to the insurance company. The expected value is ​$nothing. ​(Round to two decimal places as​ needed.) Which of the following interpretation of the expected value is​ correct? A. The insurance company expects to make an average profit of ​$31.8131.81 on every 24 dash year dash old24-year-old female it insures for 1 month. B. The insurance company expects to make an average profit of ​$349.87349.87 on every 24 dash year dash old24-year-old female it insures for 1 year. C. The insurance company expects to make an average profit of ​$256.66256.66 on every 24 dash year dash old24-year-old female it insures for 1 year. D. The insurance company expects to make an average profit of ​$23.3323.33 on every 24 dash year dash old24-year-old female it insures for 1 month.

Answer 1

Solution:-

Given data:

Suppose a life insurance company sells a ​$260,000 ​one-year term life insurance policy to a 24​-year-old female for ​$350.

The probability that the female survives the year is 0.999641.

Here we have to Compute and interpret the expected value of this policy to the insurance company.

(i) :-

Here we know that, the insurance company doesn't have to give anything if the female survives (i.e with the probability 0.999641)

And also, the insurance company has to give $260,000 if the female dies ( i.e with probability 1-0.999535 = 0.000359 )

Then,

Expected value = $350 + [ ( 0.999641 * 0 ) - ( 0.000359 * $260000 ) ]

= $350 + [ 0 - 93.34 ]

= $256.66

Hence, Expected value is $256.66

(ii) :-

Interpretation of the expected value is " The insurance company expects to make an average profit of ​$256.66 on every 24 -year - old female it insures for 1 year".

i.e, Correct answer is Option- C.