a 40 - year - old man in the u.s. has a 0.242% risk of dying during the next year. an insurance company charges $300 per year for a life - insurance policy that pays a $100,000 death benefit. what is the expected value for the person buying the insurance? round your answer to the nearest dollar.
expected value: $ for the year
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# Explanation:
## Step1: Calculate the value if the person dies
The value when the person dies is $100000 - 300=\$99700$, and the probability of dying $p_1 = 0.00242$
## Step2: Calculate the value if the person survives
The value when the person survives is $- 300$ (because they paid the premium), and the probability of surviving $p_2=1 - 0.00242 = 0.99758$
## Step3: Use the expected - value formula $E(X)=\sum_{i = 1}^{n}x_ip_i$
$$
\begin{align*}
E(X)&=(99700)\times(0.00242)+(- 300)\times(0.99758)\
&=99700\times0.00242-300\times0.99758\
&=(100000 - 300)\times0.00242-300\times0.99758\
&=100000\times0.00242-300\times0.00242-300\times0.99758\
&=242-300\times(0.00242 + 0.99758)\
&=242-300\times1\
&=242 - 300\
&=- 58
\end{align*}
$$

# Answer:
$-58$

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Explanation:

Step1: Calculate the value if the person dies

Step2: Calculate the value if the person survives

Step3: Use the expected - value formula \(E(X)=\sum_{i = 1}^{n}x_ip_i\)

Answer: