Question

suppose a life insurance company sells a $170,000 1 - year term life insurance policy to a 20 - year - old female for $270. according to the national vital statistics report, 58(21), the probability that the female survives the year is 0.999544. compute and interpret the expected value of this policy to the insurance company

the expected value is $
(round to the nearest cent as needed.)

Explanation:

Step1: Define the two cases

Case 1: The female survives. The company's gain is the premium, $x_1 = 270$, and the probability $p_1=0.999544$.
Case 2: The female does not survive. The company's gain is $x_2=270 - 170000=- 169730$, and the probability $p_2 = 1 - 0.999544=0.000456$.

Step2: Use the expected - value formula

The expected - value formula for a discrete random variable is $E(X)=\sum_{i = 1}^{n}x_ip_i$.
Here, $E(X)=x_1p_1 + x_2p_2$.
Substitute the values:

$$
LATEXBLOCK0
$$

Answer:

$192.48$