Respuesta :
Answer:
The expected value for the insurance company is $392.20.
Step-by-step explanation:
The expected value of a random variable, X is:
[tex]E(X)=x\cdot P(X)[/tex]
It is provided that a life insurance company sells a $100,000 one year term life insurance policy to a 30-year old male for $475.
The probability that the male survives the year is, P(S) = 0.999172.
Then the probability that the male does not survives the year is:
P (S') = 1 - P (S)
    = 1 - 0.999172
P (S') = 0.000828
The amount the company owes the male if he survives is, S = $475.
The amount the company owes the male if he does not survives is,
S' = $475 - $100,000 = -$99525.
Compute the expected value for the insurance company as follows:
[tex]E(\text{Insurance Company})=S\cdot P(S)+S'\cdot P(S')[/tex]
                   [tex]=(475\times 0.999172)+(-99525\times 0.000828)\\=474.6067-82.4067\\=392.20[/tex]
Thus, the expected value for the insurance company is $392.20.
